But it would also descend because the vertical component of lift would no longer equal the weight. Up elevator till the vertical component of lift again equals the weight will now prevent the descent. However, the now increased horizontal component of lift will increase the rate of turn and because the drag has been increased and the power not increased the aircraft will slow down till the drag again equals the thrust...
Yep yep yep. Yada yada. Agreed. My point is that a plane
will turn (albeit a descending turn) without any increased effort from the elevator.