I butterflied mine, which made it cook pretty fast and makes it so the thighs cook in the same time as the breasts. 3 hours at about 300-325 for 14 lb bird. If you leave it whole, probably would have been like 5 hours (whatever those timer calculations say for oven roasting would be the same time/temp/weight for smoking if you truss it the same way). But always base it on temp not time.
I'd go easy on the smoke. A little goes a long way. I used a full chimney worth of charcoal (only lit a dozen briquettes and let those ignite the others throughout the smoke), but only added two fist sized chunks of wood at the beginning and that was it. I use my Weber grill with an insert, not a standalone smoker. And I pulled it a bit early (about 155 deg) and finished it in the oven under the broiler to get the skin extra crispy.
Just drink the beer, don't put the can in the turkey.
Wanted to share how it went.
Brine I used was great. Some cider, salt, brown sugar, orange peel, bay leaves, fresh rosemary, peppercorns, water. It's the second time I've brined a turkey (or cooked a turkey for that matter). If you don't brine it, you're doing it wrong. Really seals in the juices. You can use an injector, but poking holes in your meat is big no-no, IMO.
Took about 5 1/2 hours at 300 in the smoker. I kept the smoke up throughout, but spritzed it with butter every hour to keep it golden and moist. By the 5th hour, it was getting past golden. So like you said to go easy with the smoke, i would probably let the last hour go without smoke. I'll also try to butterfly ( or spatchcock i think it's called) next time. The legs and thighs were just the slightest bit underdone when the breast meat was perfect. I finished them in the oven for another 30 minutes while I carved the breast and got the rest of the meal served. No big deal.
Against your judgement, I did the beer can. I didn't notice a difference. It didn't have a beer flavor, It was moist enough likely from the brine and the spritz. When I took the can out its still had plenty of beer in it, as if it didn't steam away to keep the moisture up. Probably didn't get hot enough inside the big turkey to make a difference. Don't worry. I had plenty of other beer to drink.
Kept a pan in the smoker for drippings which I made gravy with. No joke, best gravy ever. Had the smoke flavor in it. I could have sipped it from a glass it was so good.