If I remember correctly the stop at plymouth rock was, in all reality, like a giant beer run. Because fermentation makes water safe to drink people drank (fairly low alcohol) beer instead of water. I have read anecdotes that suggest the Pilgrims constructed a brewery before they built a church.

Hard cider was a common drink in the colonies and was drunk by the pilgrims however not (in most cases) to the point of drunkenness . This is not to say that some people there weren't getting drunk of course.