Absolutely not. Other way around. Knobbies and even inverted tread patterns provide zero benefit to traction on paved surfaces. A slick tread provides the maximum possible traction and minimum possible rolling resistance. However, the rear tire is less likely to "wash out" in any case. The critical tire for cornering traction is the front tire. If you are cornering aggressively, it is much worse to have that knobby in front, since they often lose traction unpredictably and very abrubtly, and always at lower speeds and angles than their slick counterparts.

There are plenty of good reasons to put differently sized tires on the front and back. And so far as I know, there is no rule against mixing different tire makes and models on your bike, either .