I think it's deeper than that.
Given that Mueller is acting as a "principle officer," Rosenstein doesn't have the Constitutional authority to appoint principle officers, only the President does.
Therefore, the matter doesn't even get to the Senate (which would be highly likely to confirm) if the President declines to appoint Mueller in the first place.
-PJ
Here’s a similar take in case you didn’t catch it:
http://thehill.com/opinion/white-house/388886-the-mess-rod-rosenstein-made