I would be very wary about covering them if they are old as the polystyene tiles that were very popular during the 70s were notorious for the speed they burnt and the noxious fumes they gave off. I would rather be safe then sorry if the worst ever happens. When I took ours down I remember that once I had one down to give me an edge the others came down very with no trouble at all. Still if they are modern tiles you may be ok ,but as I've said I'd think carefully about leaving them up
We took the tiles off our bedroom ceiling , not a hard job , then we sanded it , then painted it . The sanding was the dirtiest job , but the end result was good.
Plasterboard inhibits fire - 2 layers of it is an accepted way of getting a 30 minute fire protection barrier, so I wouldn't be too worried about a tile sandwich with plasterboard each side. More of problem is attaching it to the ceiling. Plasterboard must be screwed at regular intevals and you are going to have to use extra long screws to go through the 2 layers of board and one layer of tiles to get into the wood of the ceiling joists beyond that. Otherwise I don't see it as a problem.
I would say that if you fix p/board to the tiles, apart from the possible fire risk (as paddywak pointed out), you are relying on the strength of the tile fixing cement to hold the considerable weight of the boards. Easy and safer to strip them off!