Can a reverse follow a 2-over-1 response?
There are a few answers to this question :)

First, technically that is a reverse, though it does not necessarily show extras. The best definition of reverse I've seen is "A non-jump rebid by opener that would force responder to give preference at the three-level." So in the example you gave, if partner prefers diamonds to spades they would have to bid 3D, making it a reverse.

However, what you're really asking is: Does a reverse after a 2/1 response show extras? Here, it depends strongly on partnership agreements. You do not say what system you are playing, but I will assume that it is either Standard American or the related 2/1 Game Forcing.

If you are playing Standard American, the Yellow Card booklet says that a reverse still shows extras, but some partnerships modify this agreement.

If you are playing 2/1 Game Forcing, there's two different types of auctions to consider:


1D-2C: This auction bears special discussions since there isn't a particularly widely accepted standard treatment. As an example of the variety of opinions, see this thread on BBO about 1D-2C.
1M-2m: I'm going to sound like an echo, but partnership discussions apply. My sense is that most pairs play the reverse as not showing extras, although my preference is to play that it denies a dead minimum.


Rebids after reverses are in general a field where I find most beginners and intermediate players have a different idea of what is "standard"; I strongly suggest discussing this situation with any new partner you sit down with, or at least do as Marty Bergen suggests, and pray they don't come up.