I've seen some of our cats get carried off by owls before.
NOT FUN.
If they can carry off a cat, they can for sure carry off a rabbit!
When we had chickens, we had to put a mesh fencing as a roof so no hawks could take them away.
We only had a rabbit once and he was outside. Mr. Buns definitely had a mesh enclosure and was well protected when he was outside. He didn't really get to go out unless someone was watching him.
Just be careful! Hawks and owls are remarkably tricky and know how prey thinks and acts.
Rabbits are fun though. Mr. Buns was awesome.
I'll put it this way...Owls prey on rabbits/hares in the wild(Hawks to but less so because most rabbits are nocturnal) so yes they definitely will if they don't have a cover. Also I wouldn't recommend mesh.
Rabbits are food. Everybody wants a rabbit dinner. So it is up to you to protect them from predators. I am in the camp that believes in a 1 sided barn, other 3 sides securely wired up, with hanging wire cages.