Open for weeks at a time???:E I don't think so. I'm pretty sure that it wouldn't take weeks to realize you have a major and very stinky problem.
When traveling, I typically put about 5 gallons of water in both tanks along with a cup full of laundry detergent (Oxy-Clean) and a cap full of Calgon. Upon arrival at our destination and during the setting up procedure, I'll drain both tanks and add a little fresh water (about another 5 gallons) of fresh water back into the black tank.......and then CLOSE both tank drain valves.
The ONLY rv'ers I've ever heard of who left their black tank valve open are 1st timers as that 1st time will usually educate them in the correct procedure. :o
Ron