On my new VC board I wanted to add some vultures or crows, if I use Reaper models can that "disqualify" my board or cost me painting points at a GT?

Also what if I don't play with a model like the Avatars of War female vampire but I have her displayed on my army board?

What would happen at a GW sanctioned tourney (like a GT) in both of these situations?

My guess is that using another companies minis as pure decoration wouldn't matter, but I'm thinking using the Vampire model, even if I don't actually game with it, might piss people off. Looking for answers from people who've been to GT's or have run them, thanks! :)

Depends on the tourney, depends on the rulespack. In general, for GW GTs it's all GW or converted. Anything independent tends to allow a lot more, but it depends on the details.