Your story seems incomplete. Did your girlfriend talk to anyone or did the chief pilot just see you and her walking in the school? If he just saw you walking in, then it is no big deal. If your girlfriend confronted anyone and rubbed them the wrong way, then the only thing you probably have to worry about is what your future coworkers think of her.
If they told you to look for a place to live, they wanted you to work for them. I don't think they would un-hire you even if she did walk in to ask about benefits. If they do decide to un-hire you without telling you over that, you don't want to work there anyway.
Also, waiting until 15 minutes before the chief pilot leaves on a Friday is not the best time to talk to him. Wait a few days and try to call him in the morning or mid afternoon. Most people do not answer during lunch or at the end of the day.
If your girlfriend actually spoke to someone there and was anything other than polite, I would be a little nervous/embarrassed, but if she didn't get a chance to speak to anyone or was pleasant when she did, don't sweat it.