What you are suggesting is not only illegal, but very hard to get away with.The immigration authorities question you separately about your relationship to make certain it s real. Moreover, you must be married for a period of time - and LIVE together - before you get your green card.It is highly unlikely that you can pull this off. Find a better way (a more legal way) to get a green card.
Don t do that to a woman, trust me. My mom married my dad for the American nationality and now my life and theirs is insane!
That s fraud.