They must be able to get married in that state, not just have their marriage recognized from elsewhere.
Betting hard on NO for this one since polygamy (unlike gay marriage, which I assume some are using as a touchstone) isn't just a matter of political acceptance followed by changing a few words in otherwise very standard marriage laws - the whole institution of modern marriage and the entire body of law associated with it is predicated on marriages having exactly 2 participants, and changing it to allow for N participants would be a massive legal headache. In order to justify the effort there would have to be way more in the way of serious pro-polygamy advocacy and outside of a few quite small cultural bubbles I don't think the will is there at all to pull that off in the next 12 years.