Hmm, my guess is that it would have to be something with true free will, not a slave of its nature like many (if not most) of the bugaboos are. The Denarians have a very specific connection to humanity's free will by way of the Almighty, so whether or not they can make a connection with anything that's not at least mostly human is questionable. Largely because of theological themes like the importance of human free will to Heaven.
I'd imagine true fae and vamps are out. Fae because they are "primal" beings of their own supernatural nature, and vamps because they already have a "demon in residence". Dragons, NO. Temple dogs, probably not, they already seem to be spirits inhabiting a "not quite normal" shell. Werewolves like the Alphas almost certainly could since they are technically just minor spell-casters. Ghouls, probably not, already a monster. Half-vamps, maybe, I suppose it depends on if the demon has really taken residence at infection or if that only happens at full vamp. "You went full vampire! You never go full vampire!"
It's a murky area of theological/metaphysical territory. I'd say something that is "at its core" human and not already hosting something potent (like a vamps demon or a loup-garou's curse) probably could be inhabited.
