Is there any way to verify this assumption for the dept. you're applying to?
schools will see an out-of-state applicant as more desirable
This notion obviously runs contrary to your sensible expectation that a department that is trying to hire adjuncts for next fall (is that the sort of position you're applying for?) is likely going to ignore anyone who seems to be based 2,000 miles away. It means that they might not even read the letter carefully enough to see the "but really, I'm just down the street! It would be super-easy to interview me!" line at the end of your letter.
I guess we're dealing with a lot of hypotheticals, but if you're applying for a job for next fall, give your summer address.