Oak is a pretty common wood, not sure how much the wine soaking will or won't come through.
I'd experiment with say some chicken, use some chunks and experiment (it needs to dry, if it's still "wet" with wine, it will smolder, not smoke)
Normally I see people will use Oak for everything or Oak for use the heavy meats (beef, big cuts, etc) but it's not like the wine guys who only do red with beef and white with fish.
It's really a function of your taste buds, rubs, etc.