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Fairly certain it exists until he's killed on your realm, so you should have plenty of time. In the same fashion that the statue in the center of Dalaran popped up when the Lich King was first killed on your realm, I imagine Deathwing will be flying around until he's killed.
Blizzard already answered this:
Q: So does this mean he's going to strafe zones all through Cataclysm until the 4.x patch when he's killable and he's dropped on a realm sometime?
A: Yes, this isn't a permanent event, but will last so long as he's free to roam the world.
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