We have a more general question about the humidity resistance of Mod Podge here.
Mod Podge is "somewhat water resistant, but not waterproof". As Elmy points out in the answer to the linked question, you might want to opt for Mod Podge Outdoor, or a similar product that's intended for more humid circumstances, but do note that:
Mod Podge Outdoor is not waterproof. Nor does it offer complete protection against the rays of the sun. The formula does make your project very water and UV resistant. So you can put your projects outside, but long-term exposure to the sun and rain will eventually be harmful. For projects that aren’t exposed to the elements 24 hours a day, Outdoor is perfect. source
In a barn with high humidity this might still work.
However, a potential problem with your particular craft is that the string itself could be highly sensitive to humidity, as it will absorb water, expand, and consequentially transfer this water internally. Even when attempting to cover the entire surface, I'm pretty sure (in theory) that it will remain susceptible to moisture. I have no experience with the craft or type of work, but can imagine it will lose shape because of this, so I would still recommend using a waterproof sealer in addition to the Mod Podge or equivalent. Someone here recommends Rustoleum Clear Spray, so that might be a good starting point. Good luck!