It will probably work. It will not work well.
Leaving the fancy chemistry out of things, isopropanol and ethanol (grain alcohol) are pretty similar in terms of how they work as solvents for substances like thermal grease. Isopropanol is a little better, though, and there's more water (worst of all three for this work) in your vodka than there is in even cheap 70% isopropyl alcohol. Your vodka should work better than water, but worse than isopropanol.
It will WORK for the same reason isopropyl alcohol does: you don't need a very good solvent to do an adequate job of cleaning off a heatsink. Since most of us use a cloth of some sort (rag, lens wipe, coffee filter, whatever) to wipe off our heatsinks, and since it's fine if there are traces of the old grease left after cleaning, the ability of the solvent to actually dissolve the grease is not critical.
Even if it worked as well as it possibly could, though, I'd still recommend against using it. Grey Goose is too damned good to waste as a solvent.