Do adding high thrust in plane prevents it from stalling?
Every aircraft can be made to stall with a combination of low speed, rear c.g. location and high load factor.

Thrust acts in the airplane's lengthwise direction. Lift acts in a mostly perpendicular direction, so whether the aircraft stalls does not depend on its thrust when lift demand exceeds the available lift capacity.

As you observe, this will not be the case in a climb. We know that lift demand is actually lower in a climb than in steady flight. So we need to look somewhere else.

The obvious case is in turning flight when the aircraft has to counteract not only gravity but also a centrifugal force. Now lift demand can grow to multiples of that in steady flight and any aircraft will readily stall if mass times normal acceleration surpasses the lift capacity of its wings. More installed thrust will only reduce the rate of energy loss in a tight circle.

Only if pitch authority is not sufficient can stall be avoided, but then the control system will not allow to trim the full angle of attack range. This could conceivably happen with a very forward center of gravity location but should place this configuration outside of certifiable limits. 

As a side note: Stall depends on more than just the angle of attack.