The answer is No. user20160 has a perfect answer, I will add 3 examples with visualization to illustrate the idea. Note, these plots may not be helpful for you to see if the "final decision" is in linear form but give you some sense about tree, boosting and KNN.
We will start with decision trees. With many splits, it is a non-linear decision boundary. And we cannot think all the previous splits are "feature transformations" and there are a final decision line at the end.
Another example is the boosting model, which aggregates many "weak classifiers" and the final decision boundary is not linear. You can think about it is a complicated code/algorithm to make the final prediction.
Finally, think about K Nearest Neighbors (KNN). It is also not a linear decision function at the end layer. in addition, there are no "feature transformations" in KNN.
Here are three visualizations in 2D space (Tree, Boosting and KNN from top to bottom). The ground truth is 2 spirals represent two classes, and the left subplot is the predictions from the model and the right subplot is the decision boundaries from the model.
EDIT: @ssdecontrol's answer in this post gives another perspective.
It depends on how we define the "transformation".
Any function that partitions the data into two pieces can be transformed into a linear model of this form, with an intercept and a single input (an indicator of which "side" of the partition the data point is on). It is important to take note of the difference between a decision function and a decision boundary.
Best Answer
This is a bit of a necropost, but if you are still interested, here is a set of general tensorflow tutorials that explain how to run things in tensorflow. It includes examples of doing linear and nearest neighbor regressions, so it should help with your original question.
https://github.com/aymericdamien/TensorFlow-Examples
In addition, here is the original tensorflow tutorial for doing differential equations in tensorflow. Gives you an idea of the flexibility of the tensorflow computation graph.
https://www.tensorflow.org/versions/r0.9/tutorials/pdes/index.html