A few years ago, a friend and I did the whole canal, from Cumberland to DC in 13 1/2 hours (we left Cumberland at 5:00 am and rolled into Georgetown at 6:30 pm)-- on mountain bikes (time included stops). We averaged around 15 mph. The bikes were a (mine) rigid 1980's vintage mountain bike, with a 46 tooth chainring, and his (a dual suspension Litespeed). I wish I had had front suspension, as my arms were pretty tired from the bouncing around, but otherwise, the bikes worked really well. We were self-contained-- had a rack with a bag on it to carry our supplies. Wore camelbacks and had 2 bottles to minimize stops. We did fill up along the way, and kept our stops to a minimum.
On the other hand, when my brother was a boy scout, back in the 70's, they rode the canal on 10 speed bikes. My guess is the tires were probably 27 inch x 1 1/4 inch (roughly like a 700x28 or 700x32) and they had no problems at all (and that was back in the days before mountain bikes were around).
My advice-- use the bike you are most comfortable with, and enjoy it. The mountain bike can go fast--keep it in the higher gears and you should have no problem-- on the other hand, what has been mentioned above is true- the paved part will be better on a road bike -- but it isn't bad on the mountain bike.
train safe-