I would hate to see them go that long without food too. Although they may survive that long without food it just doesn't sound good. A good water change right before you leave will be a good idea too.
Maybe you have a friend that could pop in and feed them a time or two while you're gone. If so, pre-measure their food and put it into a pill box or zip lock bag and hide the rest of the food so they don't get over fed and you come back to a messy tank and possibly even dead fish.
If you threw enough shrimp into the tank, and the BPs decided they loved them, what's to keep them from gorging and eating all of the shrimp in one sitting? I'd worry about the health of the BPs after that..... :shock: