Thrust - constant in direction and magnitude with a set pitch angle and power (ignoring the comparably slight impact of airspeed on thrust generated).
Weight - constant in direction and magnitude
The aircraft will accelerate or decelerate until the drag equals the thrust (drag parallell to the thrust is a reasonable simplification making it a whole lot more comprehensible)
The aircraft will accelerate vertically until it either stalls or finds a climb angle which makes the lift equal the weight at the current airspeed (again making the simplification of having the lift parallell to the weight).
So yes, within reasonable limits such as staying off the backside of the power curve, it is to be expected. Perhaps not as much by design as by physics.
Cheers,
Fred