Yes, absolutely. The prosecutor could tear someone apart on the stand, even if they are innocent, and make them look like the worst person in the world. To much of a case relies on the "gut feelings" of jurors.
Also, to be blunt, quite often, the defendants, guilty or innocent, in criminal cases, do not have the best backgrounds. This lets the prosecutor have a field day, just teeing off on them. Going back a couple of hundred years, the framers of the constitution realized this even back then, and its part of the reason we have the 5th amendment.
The rules of evidence prevent many prior bad acts evidence from being admitted or asked about. The jurors are always going to think the defendant had something to hide if he doesn’t testify. Although I’m not a criminal attorney (only one criminal trial in my career), I’ve tried a few dozen cases — hundreds of jurors — and have a pretty good feel for how they behave.