Possibility of legal polygamy thanks to same-sex marriage opponents

My clever and creative roommate, Freddy, in the course of discussing my project has determined that, due to same-sex marriages not being recognized in every state, in certain circumstances polygamy can technically be legal. That requires a bit of a qualifier, however, in that there are conditions under which bigamy is technically legal and illegal simultaneously. This is really an exercise in logic, or more precisely, the illogicality of not universally recognizing marriage between same-sex partners across every state of our fine union. His argument goes like this:

A same-sex couple marries one another in a state in which their union is legally recognized. They then travel to another state, possibly their home state, in which same-sex marriage, even that performed elsewhere, is not recognized. Their union, from a legal perspective, is null—it never even took place in the eyes of the state. Now that their union is void, one or both are free to marry, in this state that doesn't recognize same-sex marriage, an opposite-sex partner.

While illegal in the states that recognize same-sex marriage, this second, opposite-sex union would be the only legal marriage in a state that doesn't recognize same-sex unions. The relationship, then, is both legal (in some states) while simultaneously illegal (in others).

In order for this paradox to occur, the marriages have to take place in this order. Because opposite-sex marriages are recognized throughout the U.S., if already in one first, you can’t marry someone else of either sex. The same-sex marriage must be first.

Of course, this argument hinges on a state’s legal wording for conditions under which opposite-sex marriage can occur. It also hinges on the interaction of federal law with these state laws. However, if it is the federal government’s policy to allow states to determine the legal definitions of marriage for that state, then it should not interfere in state matters of opposite-sex marriage, either.

Anyway, I am no legal expert, so if anyone reads this and has a reason why it would not work, please respond. I would like to know the viability of this argument.