It happens all the time, and the state does not have to recognize the marriage as a result of the Defense of Marriage Act.
You talk as though this has been working just great for decades. Not quite. Massachusetts just legalized "gay marriage", and the ramifications are a long way from playing out.
The whole argument will be rendered moot as federal courts step in at the opportune political moment to declare some state's affirmation of marriage as a union between one man and one woman unconstitional. Already happening.
People arguing the other side here on this thread are just practicising "realpolitik", pragmatically pretending to be states rights advocates.
You in that category?