I think 50% response is acceptable only if your supervisor really doesn't care what the numbers are. To the ordinary bounds of error you would need to add plausible bounds related to response bias. The extreme tabulation is one mandated for certain satisfaction surveys conducted by managed health care plans (related by a friend in that business): every non-respondent is assigned to a "dissatisfied" category.
So my first suggestion is to devote efforts to bring the response rate up. I would do a series of pilot experiments to see how much different combinations of approaches, incentives, and questions will improve the response rate. If this is a survey that will be repeated, the experiments could yield continual improvement over time. Continuing surveys throughout the year will also provide more timely data than a once-a-year survey. Because the sample size is smaller at any one time, quality will be higher.
You say you need to do a "convenience" sample, but you then allude to the possibility of a stratified sample; without random sampling, this is quota sampling. I urge you to experiment with a random sampling approach.. Don't try to aggressively follow-up all non-responders; it would take too much effort (50%!). Select a random sub-sample; after a 1 in k sub-sample, you can multiply the sub-sample respondents by k.
About the analytic remedies
I'm not sure what you mean by re-sampling as a remedy for non-response. That topic is not mentioned on the page you link to.
I take it that by post-stratification, you mean any technique that re-weights the data so that sample estimates of multiple characteristics closely resemble known population quantities. Three standard techniques are survey raking via iterative proportional fitting (IPF), calibration, and generalized regression (GREG). See Little (2007) and Sarndal (2007).
They will not touch that part of non-response related only to characteristics known only for the selected sample. For those factors, if any, you can model the probability of response and then apply inverse probability weighting.
The major problem with post-stratification techniques is that good matching of sample totals to the population totals can result in more bias for subgroups whose definitions were not part of the post-stratification. So include managers, departments, and products, if possible, among the post-stratification variables.
References
Little, RJA. 2007. Should we use the survey weights to weight? JPSM Distinguished Lecture
http://www.jpsm.umd.edu/jpsm/archived/specialevents/little_lecture/weights407.pdf
Sarndal, C.E. 2007. The calibration approach in survey theory and practice. Survey Methodology 33, no. 2: 99-119.
http://www.statcan.gc.ca/pub/12-001-x/2007002/article/10488-eng.pdf.
- Is it OK to weight back to the original, target population?
As a general rule, yes, it is okay, and indeed desirable, to weight back to the original target population. Your goal in these problems is usually to estimate an unknown population quantities that is aggregated over a stratified group. If the numbers of people in each group in the population is known (e.g., known number of males and females) then it is generally a good idea to weight the sample estimators in such a way that they account for the known sizes of the population groups. In this particular case, it may be dubious to make inference beyond the sampling frame of 35,000 people into the broader population of 50,000, but that is a separate issue.
If so, what should the weights be?
What happens to the variance estimates?
It sounds like you have a complex sampling problem, so this is a complex question that would need to be considered in light of a detailed understanding of the sampling scheme and estimation methods. However, to give you an idea of the principles involved, I will give a simpler example of a stratified sampling problem with known sizes for the population groups.
Consider the case where you have a population of size $N = N_M + N_F$ consisting of $N_M$ males and $N_F$ females. Each person has some characteristic quantified by a variable $X_i$ and you want to make inferences about the population mean $\bar{X}_N$. Suppose you sample from this population using stratified random sampling with $n_M$ males and $n_F$ females. You obtain sample means $\bar{X}_M$ and $\bar{X}_F$ for these two groups. In this case your estimator of the population mean would be:
$$\hat{\bar{X}}_N = \frac{N_M}{N_M+N_F} \cdot \bar{X}_M + \frac{N_F}{N_M+N_F} \cdot \bar{X}_F.$$
We can examine this estimator under the superpopulation approach, where the finite population is embedded in a larger model with mean and variance parameters. Under this approach it can be shown that:
$$\begin{equation} \begin{aligned}
\mathbb{E}(\hat{\bar{X}}_N - \bar{X}_N) &= 0 \\[10pt]
\mathbb{V}(\hat{\bar{X}}_N - \bar{X}_N) &= \frac{1}{(N_M+N_F)^2} \Bigg[ \frac{N_M (N_M - n_M)}{n_M} \cdot \sigma_M^2 + \frac{N_F (N_F - n_F)}{n_F} \cdot \sigma_F^2 \Bigg].
\end{aligned} \end{equation}$$
This gives you the quasi-pivotal quantity:
$$T = \frac{(N_M+N_F) \cdot (\hat{\bar{X}}_N - \bar{X}_N)}{\sqrt{N_M (N_M - n_M) S_M^2 / n_M + N_F (N_F - n_F) S_F^2 / n_F}} \overset{\text{Approx}}{\sim} \text{T-Dist}(DF),$$
where the degrees-of-freedom $DF$ are found using the Welch-Satterthwaite method. As you can see, the variance of the difference $\hat{\bar{X}}_N - \bar{X}_N$ is affected by the weighting in the estimator. Given a prior assumption about $\sigma_M^2$ and $\sigma_F^2$, minimisation of this variance subject to the constraint $n = n_M+n_F$ can be used as an optimisation problem to find the optimal sample sizes for the strata.
Best Answer
The short answer is yes: Survey Monkey ignores exactly how you obtained your sample. Survey Monkey is not smart enough to assume that what you have gathered isn't a convenience sample, but virtually every Survey Monkey survey is a convenience sample. This creates massive discrepancy in exactly what you're estimating which no amount of sheer sampling can/will eliminate. On one hand you could define a population (and associations therein) you would obtain from a SRS. On the other, you could define a population defined by your non-random sampling, the associations there you can estimate (and the power rules hold for such values). It's up to you as a researcher to discuss the discrepancy and let the reader decide exactly how valid the non-random sample could be in approximating a real trend.
As a point, there are inconsistent uses of the term bias. In probability theory, the bias of an estimator is defined by $\mbox{Bias}_n = \theta - \hat{\theta}_n$. However an estimator can be biased, but consistent, so that bias "vanishes" in large samples, such as the bias of maximum likelihood estimates of the standard deviation of normally distributed RVs. i.e. $\hat{\theta} \rightarrow_p \theta$. Estimators which don't have vanishing bias, (e.g. $\hat{\theta} \not\to_p \theta$) are called inconsistent in probability theory. Study design experts (like epidemiologists) have picked up a bad habit of calling inconsistency "bias". In this case, it's selection bias or volunteer bias. It's certainly a form of bias, but inconsistency implies that no amount of sampling will ever correct the issue.
In order to estimate population level associations from convenience sample data, you would have to correctly identify the sampling probability mechanism and use inverse probability weighting in all of your estimates. In very rare situations does this make sense. Identifying such a mechanism is next to impossible in practice. A time that it can be done is in a cohort of individuals with previous information who are approached to fill out a survey. Nonresponse probability can be estimated as a function of that previous information, e.g. age, sex, SES, ... Weighting gives you a chance to extrapolate what results would have been in the non-responder population. Census is a good example of the involvement of inverse probability weighting for such analyses.