An aircraft with side-by-side seating but only one person aboard should fly banked. Banking decreases lift and more elevator is needed than in leveled flight which increases drag. Correcting the banking with ailerons and rudder also increase drag. Which is better for economy?
You might be better off correcting weight imbalance with more fuel in the opposite wing if possible. Then fly with fuel selector on both as long as you can. This should give you better economy than trimming aerodynamicly.
Notice this also true for weight too far forward or aft. Good balance helps in the air.
Based on your question, you are correct: It will take more fuel to fly at a constant angle of bank.
If your goal is to remain at a constant altitude for as long as possible it would be better to fly straight and level, properly trimmed with the ball centered, than to orbit in a circle at a constant angle of bank with the additional elevator trim required to maintain altitude.
You are really describing a banking tendency no? If the airplane is banked, it will turn. To make it fly with bank, without turning, you have to use opposite rudder, creating a sideslip, which you would never do.
So if you have a banking tendency, that is the airplane wants to roll in a certain direction all the time, is the banking tendency happening while the airplane is flying straight (ball centered) or is the banking tendency because the airplane is skidding (ball offset).
If you center the ball with rudder, so the tail is lined up behind the nose, and the airplane still wants to bank if you let go of the ailerons, you have either an unequal lift problem (something in the wings is not symmetrical) or a lateral weight distribution problem.
The options are to hold aileron input, with the ailerons displaced from neutral, to counteract the rolling tendency, or counteract the rolling tendency with lateral weight offset that results in the airplane flying level with ball centered with no aileron displacement.
From an efficiency standpoint, you want to avoid flying with controls displaced into the airstream, so it's more efficient to use weight offset to counteract a rolling tendency if offset is able to achieve wings level without displacing the ailerons. On a lot of airplanes you can achieve this with lateral fuel differentials when it's possible to feed from one tank or the other. You can create a deliberate fuel imbalance that counteracts the rolling tendency, then maintain this imbalance by switching back and forth as fuel is burned. I do this in my plane because it is quite sensitive to lateral balance.
If I understand your question, it is that having a single occupant aboard offsets the CG from the longitudinal axis of the aircraft causing a slight roll of the aircraft until the CG again aligns itself along the longitudinal axis.
This is, at least technically correct. However in most aircraft design features such as pendulum effect, preset trim tabs and dihedral angle of the wings largely diminish this to the point of being imperceptible to the pilot. You won’t even notice a difference flying solo as opposed to an even number of passengers aboard.
Whatever effects associated with this are nothing compared to the effects of overbwnking tendencies, left turning tendancies eg P-Factor, torque, spiral slipstream and propeller gyroscopic precession, thrust asymmetry from an inoperative engine(s), etc. these maladies are usually corrected by means of trim on larger aircraft or dampened out by flight control computers.
So yes, to be sure, the asymmetric loading from a single pilot does try to roll the aircraft slightly, which has to be countered with a roll torque opposing it which has additional aerodynamic consequences associated with it. It it’s so minor and countered by inherent design features for positive static and dynamic stability that you won’t even notice the difference in flight.