I always cover them. It's not just rain that gets in the boat. Road grime is not fun to clean.
Here is what I do, in fact it's what I did to the boat he just bought.
Lowe's sells rolls of 2ft cellophane (in the packaging section).
Place microfiber towels on the corners and stress points on cover to boat.
Wrap the plastic wrap around the mid section of the boat and over the towels several times (where the cover hits the boat).
Cover boat with the Nautique cover. Like Shane said, it's made to be towed.
Slip a towel in between the bow stops and the cover so it doesn't rub a hole.
This should prevent any scratches. Even if it doesn't, I would rather buff a scratch than get road crap stains out of carpet and vinyl.