No, you do not pay FICA. If your spouse makes an election to treat you as a resident, for Social Security and Medicare Tax Withholding purposes, you are still considered as a nonresident hence do not need to pay FICA.
Would you mind providing any support you have for this determination? I have found conflicting information on this topic and nothing clear cut. It seems that the election to be treated as a Resident Alien can only be made for the entire tax year. If one is deemed to be a Resident Alien for the entire tax year, is there something that exempts them from a tax that is otherwise assessed against all Resident Aliens?