You have two same masses, one non-deformable and the other plastically deformable. You exert the same force for same time. Will they move with the same speed? Obviously the one will deform and move, while the other will only move.
Newton's 2nd Law says that F=ma. This law says NOTHING about the physical properties of the object that you are accelerating. Thus, the answer is "yes", the two objects will accelerate at the same rate, so if they start at the same velocity, they will continue having matching velocities as long as they experience the same acceleration.