I've flown a transmitter without any spring tension on the right stick, no springs left in it actually. (was modifed for a pan/tilt camera and I just needed to put a trainer up in the air on that freq for a quick flight...)

anyway, it is VERY, VERY difficult to fly without centering, and very tiring. you are constantly fighting it, basically the same fatigue you get from flying a very twitch heli. as others mentioned try adjusting tension, probably increasing it, and make sure your plane is well trimmed. you should let go of the sticks and it should either continue on exactly as is or slowly self correct, depending on the plane.