Does using Staff of Magnus (or any Staff) on peaple/Eye of Magnus increases the player character's skill & level? Like Destruction or something??

I've never been this far in the quest before and I was reading, it went something like the Staff of Magnus took heath from enemy then when depleted does Destruction damage or something, its really weird.

The Staff of Magnus will begin to drain Health when a target has been depleted of Magicka, but no Staffs will cause a Skill Gain when used on Opponents in Vanilla.

Recharging a Staff does count towards the Enchantment Skill.