Absolutely. You can buy a jackshaft kit, which replaces the bicycle's front crank and runs the engine's power through the bicycle's existing gears.
I've seen people getting up to 55-60mph with gear kits like this, and they start from a stand-still using the engine's regular clutch... so they still start the same.
Another option for adding some fuel economy, get up and go, and top speed, is to use an engine out of a little dirtbike with a CVT transmission (and a kickstart). I plan on building myself one of these with a 50cc 4 stroke engine from a dirtbike with a CVT transmission and an auto-clutch. with the CVT the engine can be even smaller and ends up working better.