Does pumping fuel to each wingtip affect roll trim in a stabilized turn?
Not if the fuel pumped to the wing tips in equal amounts so that the lateral CG is unchanged.  But... there are effects related to the inertia of the fuel mass (the wings become spokes in a flywheel, you could say).

I have some flying time a plane that has all of its fuel in the wing tips, in tuna fish shaped tanks, 25 usg per side.

The difference in handling qualities with the tips nearly full and the tips nearly empty is all related to inertial effects of the fuel mass; roll rate, roll inertia, yaw inertia, and roll response to yaw.  The roll rate you can generate by skidding the plane is much lower with the tips full.  The influence of dihedral in damping and restoring roll deviations is reduced.  Disturbances are amplified because of the flywheel effect of the tip mass and this is especially noticeable in yaw; there is more of a tendency for the tail to wag in bumps.  

But in a stabilized bank in smooth air, the amount of fuel in the tips made no difference in increasing or decreasing overbanking/underbanking, except to the extent that the interia of the fuel dampens or inhibits the usual restorative forces.  So if you had an airplane that can be banked and holds the bank angle with no input, there is no major effect of fuel in the tips in changing that characteristic, until you hit a bump and the inertial effects start to work.  However, where the airplane has an overbanking or underbanking tendency, the flywheel effect will inhibit it starting and tend to keep it going once started.

So to answer the basic question, if you had a plane that naturally wants to roll out of a turn when inputs are removed, the effect of fuel in the tips will be to reduce that effect somewhat, so it will still roll level but take longer, and once level it will tend to overshoot more.  It it wants to overbank into a spiral dive, same thing that way.