It is possible, with some setups, to bind the bearings, but those "some" setups are very few. If you pull a wheel out, you'll see that the part of the hub assembly which abuts the inside of your dropout is actually attached to the hub axle, so when pressure from the QR is applied, it's applied axially on the ends of the axles. This causes compression in the axle, which will result in an increase in diameter of the axle (described by Poisson's Ratio). The increase in diameter, if large enough, can start to bind bearings. As I mentioned though, this rarely a problem. More accurately stated, it shouldn't be a problem at all.
New cyclists (and some experienced cyclists) tend to make one of two errors with their QR's: they either tighten them too much or don't tighten them enough. The amount of pressure applied by the QR doesn't have to be a lot. Fastening the QR properly should leave a slight impression on your hand.
If you've been closing your QR's properly and you're still experiencing excessive drag, it may be that the bearings in the hub are either in need of service or are crapped out.