Hmm, must be regional indeed. Most barbeque restaurant around here do pork, beef, chicken and turkey. It's my normal go to at the restaurant we are going to tonight. We'll be getting dinner when we pick up our Thanksgiving dinner (at the same place)Nope - never even seen smoked turkey (in any form) on a restaurant menu.
Anyway, ours will be smoked turkey and ham, which we will heat to eat. I like to sort of steam it warm using a foil pouch in an oven
All kinds of "regional" going on! BBQ is not a very prominent cuisine here at all. There are maybe two BBQ places in our entire city (1.4 mil pop), if they're both still open. They may well have it on the menu but I've never been to either of them.
OP, let us know how the turkey turned out.