this means it's a champion that can be used in a fusion and unless it's a one time and/or time limited fusion, that blue swirl stays there forever

It's not the fusion swirl. It's a circle with a checkmark in it and I cannot use this champion for any battles.

Got a screenshot?

Ah, it means your champion is in the sparring pit. If you want to use them, just click on them from that screen and it'll let you remove them from the pit and use said champion in whatever content you want to use them in.