Well, yes.
But only if it allows a State to define Marriage in the traditional sense as well.
I don't believe there is a Constitutional basis (but, certainly there is a moral, cultural and historical basis) for the Federal Government to define Marriage.
Not without an Amendment that says they can.
If the vast majority of the nation wants that, they can make it happen.
According to Article V the Congress and the President don't even have to be involved.
The federal government has to define marriage for itself though.
People forget that millions and millions of Americans in the military and federal employment, and for immigration purposes, and even for foreign aid, that the feds have to have their own definition of marriage.
President Obama made a decision to allow gay marriage in the military, and in fact recognized it for the entire federal government.