Can a small plane be floated off of an aircraft carrier?
As far as I'm aware this has never been attempted (and I doubt the Navy would let me try - though I'm certainly game if they are!), but:


A Piper J3 Cub stalls at 38mph (33kts). 
The USS Enterprise (CVN-65) had a maximum speed of 38.7mph (33.6kts).


So, given a lightly loaded cub and an Enterprise-class carrier at flank speed, it is at least theoretically possible to float that aircraft off the deck (if it were lightly loaded, and thus had a lower stall speed).  

Achieving zero relative motion would require a little more effort - specifically you'd have to seek out a headwind, and the Cub would have to be operating at an airspeed above stall, but still pretty close to it.
For example, if the Enterprise were making 30 knots and steaming into a 10 knot headwind the relative wind on deck would be 40 knots. That's enough to lift the Cub, but as soon as it was in the air it would need to pull itself along (via its engine) to maintain that speed. The Cub would have zero relative motion above the deck at an airspeed somewhere around 40 knots).



As a (slightly ridiculous) bonus: The Belite Superlite has a stall speed of 28 mph (25kts). It would be theoretically possible to fly such a plane like a kite from an aircraft carrier. Its advertised takeoff and landing distances (both ~500ft) are also such that it could operate from a carrier deck without need for the catapult to launch or arresting wire to stop.