Does being out of trim affect drag?
Normally not; details depend on the control system and by how much the aircraft is out of trim. The force produced by the empennage will be the same in the trimmed state and when out of trim, only the control forces are different.

Let's examine the different possibilities:


Adjustable spring (as used on some light aircraft and gliders): The elevator deflection will be identical to the trim position, so there is no difference at all.
Trim or servo tab on the elevator: The tab deflection will be different, but the elevator position will be practically identical. For tab angles of less than 10° relative to the elevator there should not be any difference in drag.
Adjustable stabilizer: Now the elevator deflection will be different, and depending on the trimmed state the deflection angle might cause higher airfoil drag. If the elevator deflection relative to the stabilizer is more than 10°, a slight drag increase can be expected.


If the power consumption of the autopilot is higher in the out of trim case, this might cause higher generator loads and more engine power is needed to keep it powered. But this effect should be very small.