In a word Yes
I believe the only pieces of gear that can not be anointed are Class Mods and Relics. I would guess this is a balancing choice with how much extra power a player already gets from a legendary relic or COM they would just be absurdly strong If they also let you get them anointed.
I have a green Homing split grenade which pretty average stats but its anointed effect is 200% gun damage for a few seconds after action skill end. I used a Rakk attack build on FL4K that makes this grenade a huge part of my gear comp as I don’t need to be holding a specific gun when I use Rakk Attack