My S2A qualifies and was already registered as a Historic vehicle which on tax renewal time online "just worked" (Very satisfying to be charged £0.00 for road tax)
My understanding on reading the guidance several times is that you don't need to do anything to register for MOT exempt status. However, note that the online checkers will show your vehicle is not MOTd. This might mean that the auto-pinger fitted to police cars could get you pulled for driving without. One hopefully assumes things will get sorted out before the summons appears.