I doubt very seriously that this would qualify as a 645 room.
Just because you put a computer in a room does not make it a "computer room".
(645.4)
I doubt a mini split is going to do much for him either. They usually only have a wireless remote for the controls and the two I have come back from a power failure "off".
If I was really going to hack this, I would come up with a N/C point of a relay to provide the "on" pulse and pick the relay with a voltage generated inside the AC unit. That is how I kick started the MP3 player PCs in my cars that had ATX power supplies.
You still may want to do this in conjunction with an HVAC contractor for a little legal cover.
