Interesting idea in theory, but it seems a little silly to me. You could get the same effect by adding a few drops of liquid smoke to the bottle. All they do to produce it is pass smoke through water and filter out the ashes/tar (I'm pretty sure that's all they do, don't quote me though). Exposing perfectly good booze to dry, hot air will cause a lot of the stuff you want to evaporate.
Although this does give me ideas... smoked garnishes like cherries or olives might be interesting for a manhattan or whatever else you like.
If I were to ever try this, I think smoked vodka with some smoked peppers would make a mean bloody mary. I think I'm gonna do this the next time I bbq... smoked peppers for a bloody maria... makin me thirsty just thinking about it.