Of course they'd accept.
Why would FIDE care?
Caruana is not ready yet for prime time to be considered as the main challenger to Carlsen; the ratings are deceptive. He still needs time and a lot of work on his game.
leiph18- I mean of course if they would get rid of Fide at all. LIke Kasparov did with Nigel Short.
If I had $5m I'd be trying to tempt Kasparov to play a match vs Carlsen. $2m each basic plus $1m extra for the winner. I don't think it would be enough for Gazza though.
Caruana will likely end up playing Carlsen in a match anyway at some point so no need to pay $5m to make that happen.
If they break away from FIDE and claim it as a world championship match, FIDE can remove them from the rating list and ban them from joining FIDE sanctioned events.
Suppose Caruana is backed by a sponsor and is offered 5 million dollars to play Carlsen in a match- - non Fide related- would they accept the offer? What would Fide do in case they both accepted?