Not quite. Arrancar feed off whatever they can get, from any kind of soul. The shinigami part of you is why you can't take in Hollow reishi to heal yourself, although sharing your own makes it harder, too. Um, but what you just said... Ichigo, that sounds like you're wanting to mark that arrancar - this Ggio, as your own.

That... makes it different. What's going on between you two to make you say that?