Make sure the FD limits are set properly, and put a chain catcher on it as well. Do this right away. It's not that big of a deal to adjust an FD correctly, but the chain catcher is just such a simple thing and fool-proof.

Those two things are much more important than frame protector. But it doesn't hurt at all to put some sort of protection on the drive side chain stay. But the clear think film that is usually called frame protector isn't enough imho. Get something in a color ou like that is actually designed for protecting the chain stay as opposed to the stuff that's designed for protecting the paint from incidental, minor rubbing from cables.