I think I have the answer ( Anakin can clear a Debris Cloud's stress ), but I want to throw it out there for second opinions.
Debris Clouds give stress after the "check pilot stress" step. This is still within the process of executing a maneuver, correct? I know from previous discussion of Full Throttle, that Fully Executing a maneuver takes place after the stress from the Debris lands on a ship.
Since fully executing a maneuver happens after the stress, Anakin's ability ought to be able to remove it, provided he meets his positional requirements (Bullseye or Range 1 in full arc). Now, there's still a chance of crits, but seems like a useful too to have.