Does eating rings for the intrinsic nullify the the nutrion usage that wearing said ring confers?

The standard accessory hunger (1 extra hunger every 20 turns) is assessed specifically for wearing a ring (or amulet). If you eat the ring, you're no longer wearing it, so you don't suffer this anymore.

However, conflict and regeneration (and hunger) still have an additional hunger penalty of 10 hunger every 20 turns. If you eat a ring of regeneration or conflict (bad idea BTW), you still suffer this hunger. But eating ordinary rings such as warning or increased damage only has the downside that it's only 33% likely to actually grant you the intrinsic; so make sure you have extras!

Sources: gethungry() in eat.c, eataccessory() in eat.c