I meant it as a generic name for the call - not instructions on how to call it.
I've always been taught that declaring an emergency guarantees you a clear runway,
Nope - you'll get priority to get to the runway - but if you're half an hour out, they're not going to stop using it. That would just precipitate a bunch of other problems.
I have heard military pilots mention this - perhaps on a military runway, with its lower traffic, that might happen - but not in the busy civilian world.