Can an aircraft be turned without rudder input?
It depends on the aspect ratio of the wing and the lift coefficient. Short, stubby wings at low angle of attack will not create much adverse yaw with aileron input, especially when the ailerons have differential linkage (more deflection on the trailing-edge-up side and less on the opposite side). Differential gearing is also beneficial in reducing stick forces, so many small aircraft with manual controls employ it. Therefore, turning with ailerons alone is possible with low aspect ratio wings.

Airliner wings have aspect ratios between 7 and 11, so here it is helpful to reduce the lift coefficient by flying fast and lower than at maximum cruise altitude if you want to turn with the ailerons alone. If you allow rudder movements but just want the pilot to rest his/her feet on the floor: Almost all jets have yaw dampers, that is a device which will deflect the rudder automatically such that yaw is minimized. Therefore, airliners can be flown with the feet off the pedals and still ailerons and rudder will keep the plane in a coordinated turn.

With gliders and their high aspect ratio wings, however, using only ailerons will mostly yaw the aircraft, especially at low speed when the lift coefficient is high. The wing also has high roll damping from its high aspect ratio and low flight altitude, so the roll angle achievable before yaw becomes dominant is small. The yawing condition will now create its own rolling moment due to the dihedral effect of the wing. Unfortunately, this effect counters the intended rolling motion and prevents the aircraft from turning with ailerons alone. If adverse yaw is large enough, the aircraft will not even begin to roll but will only yaw with aileron input.  Some glider pilots even apply cross controls when entering a thermal in order to maximize their rolling speed (rudder into the turn and aileron against to provoke more yaw and let the dihedral effect roll the glider).

If you find yourself in a high-performance glider with a jammed rudder, speed up in order to fly turns with the ailerons (and elevator) only. The lower lift coefficient will reduce adverse yaw so direction can be controlled with ailerons and elevator only.