Let's say that I want to gain anima upon promotion with Mahado. Would this new weapon skill effect my keywords?

might effect on maybe constitution, but.. It doesnt say that adding anima effects keywords.

It says only to become a magician you have to use either ,holy / anima / or dark.

I don't think so. The main effect that keywords have is determining your stat caps upon your promotion. If you gain a weapon, I doubt it would influence it at all.