I used to runecraft with wearing the ring of dueling, but if you do like fire/lava runes then it really helps out to have the ring in your inventory, so you don't have to "waste time" by navigating to the gear tab. So yeah, I would say that "professional runecrafters" use ring of dueling in their inventory, but also wear one, in case they forget to get a new one from bank when it runs out of charges.
This is not the case with amulet of glories though. When you make nats, you wanna make sure that your inventory is filled with as much essence as you can, to maximize the profit.