First, there's no such thing as an illegal citizen.
Second, there's no such thing as an alternative lifestyle.
But if you are asking if a marriage between a gay person and an illegal immigrant of the opposite sex would be valid if it is not consummated, that depends upon the laws of the state where the marriage took place.
If the marriage was made with the intent for the illegal alien to gain citizenship or permanent resident status, that won't happen. Marrying a U.S. citizen DOES NOT automatically confer citizenship or permanent resident status.
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