Not necessarily, because there's no law saying that AIs have to die. This changes the evolutionary calculus significantly; you don't need to reproduce if you can just keep existing and expand your power over the cosmos.

But you're right, insofar as AIs that rapidly self-destruct and never reproduce are not going to stick around long. (I think this is actually a tautology, but it's a tautology with the character of a mathematical theorem---definitely true, but not obvious or trivial.)

It's also worth considering that there are different constraints between NIs and AIs though. NIs have to change gradually, piece by piece, gene by gene. AIs can be radically overhauled in a single generation. This gives them access to places on the fitness landscape that we could never reach---even places that are in fact evolutionarily stable once you get there.