My mum was strictest with my oldest sister, who subsequently binged alcohol from her early teens to early twenties.
Middle sister would go out and get hideously drunk, with an occasional shouting match with some other girls.
By the time I came around I didn't really have any rules. I was drinking Schnapps/Malibu from 13/14, progressing to Southern Comfort, Vodka and Spiced Rum. My school year frequently had beach parties I would drink at (I could get alcohol from shops by 16 as I could use my sisters passport) and my best friend's family owned a pub so I often went round hers to drink. Yes, I had times where I was hideously drunk and hungover the next day. I even had two extremely dramatic turns (ill spare the details).
Funnily enough, as soon as I was 18 and it was legal it became boring to me. By the time I got to university I was pretty over alcohol, and I now only drink a handful of times a year, and normally only one or two drinks at that.
Neither of my sisters drink to excess. Middle sister I am pretty sure drinks less than me while my oldest only has a few social drinks maybe once a month with a meal.
So in my experience, having alcohol at a young age meant binging at a younger age, but by the time we were early twenties we pretty much left it all behind.
Probably not the best example since a lot of people don't want youngsters binging, but this is just to say it doesn't necessarily mean you will be an alcoholic as an adult.