It might be possible for alcohol-based creatures to exist, but they couldn't drink our alcohol. Or at lesat, they wouldn't be able to drink alcohol in the way that we do.
The biggest difference between alcohol and water as a solvent is that alcohol is significantly less polar than water. This makes nutrient transport more difficult, but also allows for the formation of more complex carbon compounds, which ordinarily break down in the presence of water. Furthermore, liquid water would probably be toxic to alcohol-based organisms, for this same reason. An alcohol-based organism isn't evolved for life in a water-rich environment, and the presence of liquid water would probably start to break down complex hydrocarbons in the creature.
Luckily for our alcohol-based friends, they probably live in a fairly water-dry environment. Titan is a good example of this, with the surface containing large lakes of hydrocarbons, but little to no liquid water. They'd evolve to consume heavy hydrocarbons, but likely wouldn't evolve to handle water toxicity. They'd also be adapted for life in an incredibly cold environment, on the order of −179.5 °C.
If a Titan-adapted alcohol based life form drank a glass of vodka, they would probably be horribly burned, since the freezing point of vodka is far higher than the temperatures they are evolved for. If that wasn't lethal to them, or if they could survive temperatures where vodka is liquid, then the vodka would remain toxic for another reason: water.
Basically all alcohol that people consume has large quantities of water in it, which would be toxic for our alcohol-based friends. If, however, you chose to serve them a glass of incredibly distilled, incredibly cold alcohol, they'd probably thank you and drink it as we do water. But remember, if they offer you a sip, warm it up before you try any.