On the basis of Bishops having to be 'forced' to marry a gay couple I will say "yes". If the Church can chose whom they want to marry without fear of civil suits then there is no need to be involved.
As far as I have heard the Church is already involved. I read today that the church is going around educating people on the issued, even raising money for the cause. Then some ex-mormon that worked was part of wordperfect (That is gay) is donating 1 million.
Even Brad Pitt is part of it. Source 4
I guess the battle is already on!
Wait for the earthquake in California soon.
I believe Pres. Hinkley said that the church stays out of politics unless a matter of morality is at stake, which I believe gay marriage is a matter of morality, so we should expect the church to get involved, the extent of their involvement could be debated.