Yes! If they are bitten on an extremity (arm or leg) and the limb is removed very soon after the bite, the infection won't spread. However, the sooner the better! Leave it too long and you'll turn anyway, and then you'll just be an armless zombie.

As for getting their limbs back, there are a few ways of doing this. The easiest would be dying - Hope will bring them back fully intact. However, Hope can restore a limb even to a living person. He won't do it for free, but a deal could definitely be worked out in order to get a new shiny human arm! Or, if you want to get weird, contact the other gods and see what kind of arm they might be willing to give you.