Don't say a word until you actually call out sick.

If you're sick, you are sick. Call in sick. Then, stay in the hotel, or non-rev home, or go get a room, but DO NOT jumpseat.

If you call with a head's up you're opening yourself up to a world of hurt from multiple angles, as already explained above. I know my company will pull you off when you call in to "give them a head's up" which is actually in your best interest since it is clear-cut and dry. If you think you can make it a leg, you make it a leg. If you can't, you can't. The company has reserves. You won't be the first to call out mid-trip. It sucks, but it happens. Don't make a habit of it.