Intriguing on the face of it but the fact that your drink will change (get smokier) as the ice melts takes it up a notch:
I’d worry about either too much smoke eventually or not enough ever. The flavor of smoke is so strong that it’s really easy to have too much, especially when you have to either accept that or race against the clock to finish your drink. I went to a place a while back that does some cocktails in what they call smoked glasses. They make a tiny fire on the bar (probably on a piece of stone; I didn’t notice) and put an inverted glass on top. It gave what I thought was just the right amount (a hint) of smoke on the palate of the drink, with slightly more on the nose, which was very nice.
Wow!
Perhaps starting with a drop of “Liquid Smoke” as you make each ice cube would work.
http://www.colgin.com/liquid-smoke.php
That is easy enough for me to try!