Leaving aside that Prop 8 and every other fight like it will leave a permanent impression that the church is a reactionary, bigoted organization, I think the church is going to benefit internally, no matter the outcome.
If Prop 8 wins, the church and its members will feel vindicated and believe that they have been involved in a great cause to preserve the righteousness of the nation and safeguard the sacred institution of marriage.
But if it fails, I suspect that the church will benefit even more, at least among its own members. We were taught all our lives that we were a peculiar people standing up for righteousness in a wicked world. The defeat of Prop 8 will be held up as a shining example of church members “standing for something,” despite its unpopularity in a wicked world.
Yes, there will be the occasional member whose sense of right and wrong and fairness will cause them to lose that much respect for church leaders, but those people are in the distinct minority.