There's this idea that #reddit mods resigning will be a problem for reddit because they provide free labor. I don't think that the idea is correct.
For the most part reddit doesn't care about the quality of mods past "removes obviously bad comments". PR firms, political partisans, etc will be happy to provide the free labor for reddit in exchange for the power to manipulate internet comments. Reddit doesn't have to do anything accept the people that ask for the positions and the problem goes away before it even exists.
Hyper-specialized subs that run on a model of needing expert mods like AskHistorians are the exception to the rule, but they are rare and reddit could afford to shed them.
And that's before you get to the "it's reasonably cheap to just hire mods" solution.
The real damage that the protest is doing to reddit is the loss of power-users who create content, and the significant strengthening of their competitors (like kbin, which I'm currently posting this on). Not the loss of mods (except to the extent that mods often happen to also be power users).