There are a few things to consider when answering this question.



The quality of your singing voice is directly related to the overall health of your body. If you are drinking enough to cause your overall health to deteriorate, then you are causing your voice to deteriorate as well.



However, even if you are not drinking enough to damage your health, you can still cause damage to your voice. This is true even if you do not drink enough to "feel it".



Alcohol (even just one drink) numbs your throat. This can indirectly cause damage to your voice since you need the nerves in your throat to send signals to your brain.



For example, I might have accepted a gig singing in a night club, and I am quite nervous and have a stiff drink before I go on stage. Normally, when I have not had a drink, I know when my voice is tired or when I have pushed my voice too far because I will feel discomfort in my throat. But tonight, since I've been drinking, my throat is numb. I push my voice past its usual boundaries (this may take the form of singing too loud, too high, too low, or simply for too long a time period) and I do not receive those warning signs. So I keep going, and I have just caused damage to my voice.



Now if this situation happened just once my voice will recover. But if it were to happen often, there would likely be long term damage.



The occasional drink, when you are not singing, followed by enough water to counteract any dehydration, is very unlikely to cause any damage.