It is not illegal to ASK about your marital status, but rather to use that information "against" you in making residency decisions.
First, as noted above, it is unlikely you will even be asked about a GF - if they do ask if you are married, and you respond in the negative, they don't usually ask further questions.
Secondly, also as noted above, with the exception of the most hard-core, malignant, good-old-boy programs in which it was believed that surgery residents shouldn't be married (ie, such as when a friend of mine was going through a divorce, his program director told him that he was "better off, surgery residents, especially males, shouldn't be married."
), being married is seen as a GOOD thing. Residents with a happy homelife make happier residents. Plus you get more sleep than your single buddies out stalking the local bars trying to impress chix with their medical degree.
Obviously, you have to have a supportive partner. Memorize this: you will always be home later than your first estimate. The sooner your GF realizes this, the happier she will be. Tell her that calling you every 45 minutes does not get you home any earlier.
At any rate, I see no reason to conceal the fact that you have a partner.