Taking a provider out for a lunch or dinner is something I am open to but it could get awkward if it is your first meeting and either of you discover that there is no "chemisty" there. I would also be open to just going out for a meal with no BCD afterwards. If that went well then I would definitely be coming back for some fun at another time.
I have gone out for a meal couple of times with someone I already knew and had a very good time. Once before BCD and once after. It's all good.