(Further updated answer, with a look deep down the Lion's Mouth in the last section.)
Joseph gave an answer (“No!”) to your actual question; I'll try to get your (and my) head around the “temporarily”. Let's start from TeX-by-Topic, bottom of page 129:
The \noexpand command is expandable, and its expansion is the following token. The meaning of that token is made temporarily equal to \relax, so that it cannot be expanded further.
At first I dismissed this as a colourful description, but one can easily see that TeX-by-Topic is right: The following short plain TeX file
\def\foo{bar}
\expandafter\show\noexpand\foo
\bye
prints
> \foo=\relax.
<recently read> \notexpanded: \foo
to the terminal, so \foo is indeed “made temporarily equal to \relax”. What I find very interesting is the \notexpanded: \foo; this \notexpanded isn't mentioned in the TeXbook or in TeX-by-Topic, and I only found one occurrence in Knuth's torture test for TeX. (Another test is to put \tracingcommands=2 \noexpand\foo into your TeX file; then you'll find a \relax in your log file.)
In the TeXbook there's a description that I find easier chewable than the one from TeX-by-Topic (since it doesn't contain “temporarily”): On page 214 it says
\noexpand⟨token⟩. The expansion is the token itself; but that token is interpreted as if its meaning were ‘\relax’ if it is a control sequence that would ordinarily be expanded by TeX’s expansion rules.
So what does “temporarily” mean?
In practise, “temporarily equal to \relax” means the following: When TeX expands \noexpand\foo, the result is \foo with the temporary meaning \relax, and as soon as TeX continues expanding, \foo gets back its original meaning. A typical use case of \noexpand, from Tex-by-Topic (page 130):
\edef\one{\def\noexpand\two{\the\prevdepth}}
Inside the \edef, TeX doesn't expand \two but continues with the next token { (which is also not expandable). The \noexpand is needed since otherwise TeX would try to expand \two. This would cause an error if \two is undefined, and it would cause much more trouble if \two has been defined before. (Before \def one doesn't need a \noexpand since \def is not expandable.) If you now \show the \one, then you see that the real \two, not a \relaxed one is inside \one:
> \one=macro:
->\def \two {-1000.0pt}.
What's happening behind the scenes?
Let me first say this in the picture of TeX's mouth and stomach. In general, TeX continues chewing on a token list in its mouth as long as the first token is expandable. When the first token is unexpandable, it's swallowed for further processing in the stomach. Now \noexpand indeed wraps the token following it in some protective coating. However, this coating is chewable; figure that it's made of sugar. Thus, when TeX chews on such a coated token, the coating is removed (and the token is expandable again), but TeX gets a sensory flash and thinks “Wow, this tastes like \relax, I want to swallow it.” And sure enough, if the now uncoated token is the first in TeX's mouth (think of “first” as “closest to the throat”), then it is swallowed.
Two examples (the 2nd one being rather academic):
You have, e.g.,
\edef\bar{\noexpand\foo\anothercs}
Then inside the \edef, \noexpand\foo expands to a \relaxed \foo. This is converted back to \foo, immediately swallowed, and TeX continues with expanding the next token \anothercs.
You expand \noexpand\foo twice, e.g. with
\def\foo{bar}
\expandafter\expandafter\expandafter\show\noexpand\foo
\bye
Then on the terminal you get
> \foo=macro:
->bar.
Thus, expanding \noexpand\foo once gives a \relaxed \foo (as seen above), and the expansion of the \relaxed \foo is again the original \foo. And this is not swallowed since it's not the first token!
Disclaimer: The above I found out by observation; it might be that some details are not entirely correct.
Some final remarks
Your attempt at defining \noexpand as macro fails for several reasons. One technical point is that \let#1\relax is not a good idea if #1 isn't a control sequence. Another point is that it's not really helpful to do \let#1\relax #1; this has the same effect as \relax as far as I can tell. (And as pointed out in the other answers, \let is not expandable.)
While a definitive answer can only come from the Stanford team involved in development of TeX, and from Professor Knuth in particular, I think we can see some possible reasons.
First, Knuth designed TeX primarily to solve a particular problem (typesetting The Art of Computer Programming). He made TeX sufficiently powerful to solve the typesetting problems he faced, plus the more general case he decided to address. However, he also kept TeX (almost) as simple as necessary to achieve this. While expandable macros are useful, they are not required to solve many issues.
Secondly, there are cases where an expandable approach would be at least potentially ambiguous. Bruno's \edef\foo{\def\foo{abc}} is a good case. I'd say that here the expected result with an expandable \def is that \foo expands to nothing, but I'd also say this is not totally clear. There is the much more common case where you want something like
\begingroup
\edef\x{%
\endgroup
\def\noexpand\foo{\csname some-macro-to-fully-expand\endcsname}%
}
\x
which would be made more complex with expandable primitives.
The above example points to another grey area: what would happen about things like \begingroup and more importantly \relax. The fact that the later is a non-expandable no-op is often important in TeX programming. (Indeed, the fact that \numexpr, etc., gobble an optional trailing \relax is sometimes regarded as a bad thing.)
Finally, I suspect that ease of implementation is important. The approach of having separate expansion and execution steps makes the flow relatively easy to understand, and I also suspect to implement. An approach which mixes expansion and execution requires a more complex architecture. Here, we have to remember when Knuth was writing TeX, and the fact that programming ideas which we take for granted today were not necessarily applicable in the late 1970s. A fully-expandable approach would I suspect have made the code more complex and slower. The speed impact is one that was important when TeX was running on 'big' computers.
Best Answer
You had spurious spaces, and missing
\expandafter