Gadgetopia

it looks like a pair of these:

http://www.jetcatusa.com/p180.html

would create about 90 lbs of thrust max, not unreasonable for a bicycle.

happens to be the same engines used by this guy:

http://www.jet-man.com/index_eng.html

The question is, if this bike had wings and was placed on a treadmill, would it take off?

Yes, the bike would take off, as long as: 1) the little jet engines have enough airtrust to move the bike forward, 2) that the wheels of the bike were left free spinning. 3) that the treadmill was long enough

If there was enough air trust from the little jet engines, the bike would still move forward regardless if it was placed on a treadmill or not (remember that the engines are pushing against the air behind it and not the treadmill). Moving forward would cause airflow over and under the wings, and as long as there is enough forward speed provided by the air trust, the Bernoulli effect would kick in and the bike would take off because of the pressure difference over and under the wings, creating lift.

Remember that the treadmill must be long enough to let the bike reach the necessary air speed required to create lift.