Gretch,
In fact on the 737 you do disconnect the auto thrust on the approach. Not doing so will result in the auto thrust chasing the speed with consequent porpoising.
You can leave the A/THR enagaged on the airbus because in normal law the nose will remain pointing down the glideslope regardless of any increase or decrease in thrust.
The 777, being fly by wire, also allows the A/THR to remain engaged, but it certainly insn't the case with the 737.