Can a plane bank without turning?
Yes it can. The steady-heading sideslip (SHSS) maneuver is used in flight testing to demonstrate static lateral/directional stability (similar maneuvers exist as sideslip approach in crosswind, or stabilized control with one-engine-inoperative at low speed). In this maneuver, rudder is applied to hold a sideslip, which generates an opposing side force and rolling moment. The rolling moment is neutralized via ailerons, and the side force is canceled out by banking to the opposite side. Once at steady-state, the aircraft is maintaining a rectilinear course, while banked.

Adapted from NASA IS-97/08-DFRC-01