A hint of wood smoke is an excellent supporting flavor for turkey but it should not be the dominating flavor. It shouldn’t taste like your turkey died in a forest fire. Poultry accepts smoke flavor very easily so you want to use a light hand in using smoke as a seasoning.
Avoid heavy white smoke, you want a light grey/blue or even invisible smoke. Wait until the fire is burning cleanly and the thick white smoke has cleared up before putting your turkey on the grill or in the smoker.
Be careful with your wood choices. Hardwoods like hickory and oak can be quite strong so use them sparingly. Fruit woods such as apple or cherry are a little more accommodating. Choose your woods to complement your flavor profile. I like a combination of hickory with orange and bourbon.
The Char-Broil Deluxe Digital Electric Smoker makes smoking your turkey extremely easy and does a great job imparting a light smoke flavor.