It shouldn't and probably won't, as long as McConnell runs the Senate. But I remember hearing the exact comment about the SCOTUS appointment, from I believe Schumer. The Senate shouldn't consider any appointments from Trump while he is under investigation by Mueller.
In terms of political rhetoric, sure. That's a legitimate card to play, to reduce the credibility of an opponent. Practically, though, there are plenty of political counterarguments ("still POTUS," "constitutional obligation to honor the process," "this is a good nomination," etc.) to keep the nomination on track.