Can a dentist tell you are a heavy drinker by examining your teeth?

Usually. Heavy drinking (or smoking/drugs/medication/even poor diet) can be seen by the dentist/hygienist.
Yes. Drying effect of alcohol damages teeth and gums. Heavy drinkers need more dental support, not less, especially as they tend to loose sight of their health care needs. The best thing you could do would be to get help for your alcoholism.
Sometimes. Heavy drinking dries out the mouth, causes decreased salivary flow which increases your decay rate and impedes the healing properties of the gingival tissues essentially leading to an increase in recession, root decay, and other issues. Ofter heavy drinkers don't take care of their teeth and gums which accelerates the problem as well.