I keep red claw crabs and have thought of doing this same thing before, but haven't had the chance. I found a post about a guy who tried it on monsterfishkeepers once but I don't think he ended up succeeding, he probably could have but other unrelated problems came up I think.
One problem he has was when pumping the fresh air into the cave, it would eventually overflow and come out in large bubbles splashing everywhere and making noise. I think you could fix this problem by using another air tube and making a sort of air escape where the bubbles over flow into, and are released by the air tube but it won't drain all the air from the cave.
I hadn't thought about the crabs escaping by the airline, but no crabs have escaped my tanks yet and I have airline tubes, heater wires, and filter tubes all coming in and out of the tank. You just need a tight lid and you'll be fine in that area.
I think the hardest thing will be making something that is airtight and also strong enough to resist the bouyancy of that much air pushing up on it all the time