It's hard to provide a specific answer because a lot of important context is missing from your question, but here goes.
In a conventional airplane, with any manner of control system, when the stick is released from a held position where there is deflection of the control surfaces, the stick should return to centre.
In salt-of-the-earth cable driven control systems, the act of pushing the stick in any direction causes control surfaces to move up into the airstream. The drag that this produces creates resistance, a weight that is felt in the stick. When you let go, the stick will spring back due to this resistance, and probably over centre into the opposite side and cause an oscillation, but that will dampen out and the stick will rest neutrally.
This self-aligning force can be felt when you're driving a car at relatively high speed. Imagine you're on the highway and to follow the road, you need to make a gentle
Even in systems where there are not direct connections between the stick and the surfaces, engineers add artificial means to produce this feedback. For example, in some fighter jets the stick has an extension under the floor which has a deadweight attached to it, which the pilot has to pull against to hold the airplane at a certain level of G-loading when turning.
This self-aligning force is very important to how the aircraft feels in the hand. It can also be felt when you're driving a car at relatively high speed. Imagine you're on the highway and to follow the road, you need to make a gentle curve. Then imagine you turn the wheel and it's as light as a feather.. it would be very difficult to find and hold the precise input required to produce the required turn.
In your scenario, when the airplane is climbing and the stick is released, it may fall backwards a little bit initially, but it will not accelerate like a dropped object straight to maximum deflection because the airplane itself is resisting the force gravity as it's applying itself to the stick. it will find a neutral point just aft of centre stick
None of this means to say that the airplane will climb or descend, or even maintain the same angle of bank. You haven't defined enough variables in this scenario (Airspeed, pitch angle, power setting, trim setting, engine type) to tell us what might happen next.
I will leave the autopilot part of the question to somebody who's even remotely qualified to talk about that.