I'm not sure if it was common, but there were some roadrace bikes in the 70's pwered by 2 stroke outboard engines. There is one here in Edmonton that shows up occasionally in the vintage section of bike shows- sorry I can't recall who built it or owns it presently, but it was either an act of ingenuity or craziness, depending on your point of view. It had a monocoque frame (not tubular), used the engine as a stressed member, and if my (admittitly dim) memory serves, an Earles type front fork. I believe it did ok. I have no idea what he/they used as a transmission. I also recall some drag bikes with outboard based engines. Several others used snowmobile engines. Ah, the 70's. There was more to it than wide bottom plaid pants and platform shoes.
Sounds like a project for that old Evinrude at the back of the shed