Well I think you sort of answered your own question. Suzanne Pleshette was the first person I thought of when I saw your question, also Lucille Ball and Bette Davis in their later years.

It just means a gravelly, low, deep voice. Sometimes it's natural and the person can't help it but often it is the result of drinking too much hard liqor and smoking too many cigarettes, hence whisky voice. Although to be honest smoking is nearly always the reason for such a voice rather than booze.

I don't think it has anything to do with needing to be drunk to apreciate it!! I remember my folks using the term years ago. But it is usually about a speaking voice and people with a whisky voice aren't usually goos singers as the voice tends to be monotone and flat.