I would do it. As others have said, I do not think it is a big deal as it is you who will be travelling and agree with the poster who said you may save them a checked bag fee. I would also think that depending on your status, having your number attached may help you in the event of delays or cancellations on you way to/from the interview. While the employer may not care so much about you getting back on home on schedule, they may have people and/or events scheduled for your interview that may be harder to reschedule should you be delayed on your way to the interview.
Good luck with the interview.