I think there just a few too many to do the whole lot in Patong, but what may be possible is this -
A drink in every bar down Bangla Road.
There are about 25 bars in Soi Easy, 25 Soi Gonzo, 25 Soi Eric, 25 Soi Seadragon, 20 or so in Soi Crocodile.
Then there are the big bars down the street such as Shipwreck, Full Monty, Irish bar, Tiger, rock Hard..........
You could try to do one Soi in an evening. That may be possible, but I bet after three days of it you would be that drunk you poo your pants
Have fun trying it!!