If it works, do it. Cats are mysterious creatures (my current Vet's opinion).

If the new cat Coop does not mind being Cooped up, and he feels safer, and gets some attention each day, that may be all he needs. If he or the other two starts to show stress at this arrangement, you may have to rethink.

Older adult cats sleep alot. If he feels safer that no one will sneak up on him, and vice versa for the other two then the lower stress levels all around including you are what you aim for.

Adult cats take a while to get used to new routines. Some are good at it...and others not. Some won't even accept new foods!
It has been my experience that when young and introduced to new things, places, it goes more smoothly. Traveling as we do to a summer rural setting is the opposite of what we live the rest of the year. All of our cats so far have managed with this.
But some of our cousins have more difficulties getting their cats to be comfortable there. Last summer one of our cousins' cats who was new, refused to go home and was "lost" for 3 days in fact on the island. I tend to think it was because of the dog next door who roamed free. We've had Oreo lose her way in her early days too.
But Weez last year did not go far or get lost. We don't know how Houdini will react yet either this summer.