At worst you may have to cut a little chunk out to get the spring clips through. Here’s an idea, why not cut a hole in a scrap of plasterboard, wood or whatever & give it a try before attacking the ceiling.
Hmmm..Screwfix holesaws: With the one I bought the teeth on it were so badly set it just about ripped my arm off using it! Also the collar that holds the locking plate in kept coming loose. Get a decent brand name like Starret or Bosch.
Basic deal with Screwfix is that a lot of their unbranded stuff is guff!!