Yes, it work.
I did

How sure are you about this ? The item skill states that you don't need to pre-equip the item to gain the effect (like the 10 stacks that builds up in time from gathering gear), yet you still need to have it in hand for the skill to activate don't you ?

100% sure. You just need it in the inventory.

Avalonian tool bonuses are always active from inventory, as long as they are the tools you are actively using to gather. So if you're carrying a T4 Avalonian sickle but gathering with a T7 regular sickle, you will not receive the bonus.

the game automatically equips tools when you're gathering... watch your paperdoll/inventory after clicking a node

Oooooh, so that is why your hp drops for a moment every time you farm, was wondering about that. Well, this is awesome