While I don’t know about Catholics in particular, I do know that charities that fall in-line with the values of Evangelical Christians and Mormons tend to have no difficulty fundraising or finding volunteers; while charities that are against the values of these religious groups have difficulty surviving without the aid of the government. I’m not religious, but I do know that these (often criticized) religions tend to volunteer and give to charity at disproportionate levels; and if a "Charity Strike" was started by the Catholic Church and followed by other denominations it is likely that charitable organizations would grind to a hault.
Realistically, I don't think this would happen because of the nature of people who volunteer, but I think you need to consider that many of the devoutly religious individuals see a greater need to volunteer; and as a result may be out working for multiple charities three or four nights a week, and these people are not easy to replace.
If somebody feels a greater need to volunteer and is volunteering for multiple charities three or four nights a week, I doubt they're going to stop due to gay marriage, even if the Catholic Church tells them to. I highly doubt all religions in the world are going to team up against gay marriage, or team up in any way against anything for that matter.