Personally (speaking from experience), I would pass on the barbecue sauce.
In my reverse flow the skin crisped up at 250 smoke temp, but don't worry about the skin, smoke till the bird is done and you can always crisp up the skin in a frying pan.
(I just realized my earlier post did not state the actual smoking temp of 250°, sorry.
Here's one I brushed with homemade Honey Barbecue at 155° (doesn't look very good, does it!)
the skin was crispier than it looks but I would not do it again.
You would be better to use a sweet dry rub in place of a wet sauce
Here's one with no oil butter or anything, just sprinkled some salt and pepper.
If you were doing a bigger bird such as a turkey, then a wet rub (slather) would be ok, however, I would suggest foiling the wings when they are getting dark, then foil the breast at 150°

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Cherry wood smoke
| Foiled Wings, starting to get dark | Foiled breast when thigh reached 150°F |

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| Removed all foil at 155°F and brushed with honey | Pulled when thigh reached 160°F | Rested, wrapped in foil and towels for 30 minutes and ready to carve. |