The alcohol evaporates more quickly than water, which makes it nice to work with. The layers of paint dry quicker, and the fondant surface doesn't get sticky, or at least AS sticky. You could use water, if you had nothing. But it would take longer to dry and you'd have to be careful about slapping too much on at once so it didn't drip and run or sit there and absorb into your fondant and make it soggy or sticky.
No, champagne does not have as much alcohol. If you were having to do a big area or a lot of layers, then it could get sticky on you. That's why you would have to take a lot longer to accomplish the job. Let it dry thoroughly between coats or after doing the area. Without the alcohol to evaporate much more quickly, evaporation of the water takes longer.
go bug a neighbor, nothing makes a great impression like a mother with a baby on the hip asking for a cup of vodka. 
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