In theory this should allow the non-EU citizen free movement rights within the EU as the spouse of the EU citizen. The document they would produce is a simple normal marriage certificate.
Extract from primary family member definitions:
Does anyone in same-s.ex marriage have any experience with applying (under European law) for an Visa or Residence Card? All straight forward? Are you legally married, and if so where was the marriage?(a) the spouse;
(b) the partner with whom the Union citizen has contracted a registered partnership, on the basis of the legislation of a Member State, if the legislation of the host Member State treats registered partnerships as equivalent to marriage and in accordance with the conditions laid down in the relevant legislation of the host Member State;
Note: I earlier posted on the Irish forum, but did not get a substantial reply. I hope there is more experience in the more active UK EU law community!