Can an alcohol distributor collecton a debt from a current owner that was incurred by a previous owner?

No, it is not correct as a general matter that an "address" owes the debt; the debt is owed by whatever person or business incurred the debt. However, what that means is that if you leased not just the physical location, but also took over the business in some fashion, you would in fact owe the money (or more properly, the business you took over still owes the money).

However, if the terms of the debt--i.e. the terms under which beer was sold to the bar--were that anyone taking over that bar  in any fashion would have to pay outstanding debts, it *may* be the case that you would owe--though you would very likely have a claim against the person who leased the bar to you, if he/she did not appraise you of that critical condition or fact. Similarly,if you took over the liquor license and the sale was to the holder of the license, then its possible that in taking over the license, you acquired the debt--but again, might have a claim vs. the previous holder if that was not disclosed.

Furthermore, if the lease agreement you signed states that you owe the debt, then you would--you took it over.

You should ask the distributor to send you a copy of the agreement, terms of sale, etc. under which they claim you owe. Have an attorney review that agreement as well as your terms of lease to see what you might be obligated to as well as your potential  rights against others.

Finally, note that even the distributor can't take you to court to make you pay, it's possible the distributor could simply refuse to sell you more beer, etc. unless that debt is cleared up--they have the right to decide who to do business with, unless there's a contract requiring them to sell to you. In that case, depending on what other distribution options exist, you may have no practical choice but to pay.