Yes. I have seen just this behaviour recently with high positive wind shears between the surface and 1000ft lately. If you hold a constant attitude with speed running away from the trimmed speed it will "help" you. Obviously the easiest solution is to trim the other way as that both helps you out and inhibits the system up to 5s after you let go of the trim switches.
It is working to design, just like the FD suggesting one pitches to 25° to keep speed then rocket back down to 10° the moment the wind entirely predictably steadies
