You can as long as you injection is different that your brine. I brined a turkey for a neigbor awhile back and before I smoked it, he injected the breast with melted butter and a lemon pepper marinade. Turned out great.
I always brine a turkey and then inject it before I fry it but fo smoking I just brine it and then smoke it with no injecting but i'm not the turkey God and you can do anything you wish to your bird. So give it shot and let us know how it comes out and don't forget the Qview.
If you brine and then inject I wouldn't have it sit in the fridge for more than 4-5 hours since the brine will have already begun to break down the meat and depending on your injection it may do the same.
Personally i used to brine always and all the time, if it was a bird it was dunked into a brine solution but I honestly can say that doing more injecting I have really become a fan of injected poultry and if you allow it to sit long enough it seems to be just as moist and flavorful as a brined bird with more concentrated flavors.