If the plane’s issue is the exact same issue and the mitigation is the same mitigation that’s already been approved by the FAA as effective, yes, and this is currently how things work. See the MEL. If mitigation X is approved for situation Y, then it is approved for all situations of Y (within the same context). You don’t have to go to the FAA to get a new approval to take off every time Y happens, you just do X and you’re approved.