Probably not; the average 550 size drill motor has around 100 watts of input power making it less powerful than many linac motors. the gearbox output is much lower than the un-geared linac motor so you would get a REALLY slow linear movement.

Like Mario said, bigger diameter is better for torque and to get the speed you want, a motor with a fairly high KV rating will be needed. Something like the NTM5050-580 or SK3 4956-600kv motors from Hobbyking will have way more power and speed than the average linak motor. They are also wider, so you will need to make a motor mounting plate to move the motor away from the linak body. You could draw up a design and get someone to make it, or a flat mounting plate should not be too hard to make with hand tools and a small drill press. you will also need to cut off some of the back cover of the linak and probably get a new pulley and longer belt.