Lets leave aside the issues associated with using an autopilot below its authorised minimum height (If we're talking N-reg for the moment, that is published in the flight manual supplement)
As you fly down the ILS, the sensitivity of both localiser and glideslope increase significantly. As you fly down to the runway below the ordinary Cat I DA, that sensitivity will rapidly increase to the point where is defeats the ability of GA autopilots to make the necessary adjustments with appropriate timeliness.
An altogether better plan, would be to fly the aircraft manually, with the FD displaying in approach mode. That way, you can decide if you want to continue all the way to the ground.
2D