If the motor runs fine when bypassing the overload on the bench and in the washer doing loads of laundry, then you could certainly use it but I would only do so if you are always going to be nearby and can monitor it while it's doing a load of wash. If this is a job you are doing for someone else, I wouldn't do it. If something went wrong, there is nothing to protect the motor and wiring in an overcurrent situation other than your circuit breaker which may or may not trip depending on the load. You don't have to bridge M1 and M2. Just cut the yellow wire and the orange wire a few inches from the motor, strip the two yellow wires and the orange wire that goes up to the lid switch and splice the three together, leaving the orange wire from M1 disconnected.