Nope, it's resolving hunt damage by taking corruption rather than by taking damage on the companions etc. Thematically, hiding from the hunt by using the ring increases Frodo's corruption by the ring.
When there is no other option than for Frodo to take the damage as corruption due to a hunt, just imagine that he has physically put the ring on his finger. This is taxing. Eats away at your constitution. To quote Bilbo:
“I feel thin, sort of stretched, like butter scraped over too much bread.” ― J.R.R. Tolkien, The Fellowship of the Ring