Interesting question.
I can't say for sure, but my take is it probably wouldn't, based on a couple things:
1. I've known people who work sales for companies located across the country. We don't consider these jobs "remote" like the tech world, but they're similar in most respects. They own a home in a different city than their employer.
2. Banks and brokers are, for the most part, dying to give away money. The employment section of the mortgage application often doesn't ask much more than how long you've worked at your employer and what your salary is (sometimes a letter from your employer is required, but should be no problem).
Just apply, it doesn't hurt.