Absolutely, he'll be fine to drive but the injection site will hurt A LOT for the following couple of days.

DH and I had our shots again before we went traveling in 2004. We had a funny but painful time pushing each other in the arm afterwards! It was surprisingly painful but the nasty pain didn't kick in until that night and the next day. OMG, the next day! I thought there was something wrong. The pharmacist I checked with laughed at me! Lol.