I believe you are referring to the cockpit sump drain in the boat. Usually the owner's manual for a Boston Whaler boat gives advice on how to operate the sump drain. I believe the owner's manual is available on-line at
http://www.bostonwhaler.com/boat_graphi ... ochure.pdfI searched the (above linked) document for advice on leaving the cockpit sump drain unplugged when on a mooring, but I could not find any information on that topic. Generally all references to the drain were to check that the drain was plugged. Perhaps the design of the 170 MONTAUK does not permit the drain to be left open when the boat is unattended on a mooring.
Reticence to leave the drain open is natural. Have you opened the drain and observed how much seawater enters the sump?
If the level of seawater in the sump rises only to a level that will be contained in the sump, you could leave the drain unplugged. If the level rises above the sump, and begins to fill the cockpit, leaving the drain unplugged would not be a good idea. Inasmuch as I am not familiar with your boat, please comment if you have tried leaving the cockpit sump drain open and to what level the seawater will rise.
As for adding a second battery dedicated to running the sump pump, my initial reaction is to ask how such a battery would be kept charged? It is reasonable to anticipate there might be substantial rain during a period of several days while you were away. If the battery were deeply discharged, how would you re-charge it?
Another consideration for the second battery dedicated to running the sump pump: how many hours of pump operation would be necessary before the charge was depleted? This would really be the criterion that dictates the size of the battery. You can approximate the battery capacity needed by figuring the operating Amperes of the pump and multiplying by the anticipated period of operation. For example, if the pump consumed 5-Amperes when running and was estimated to run for 8-hours, a 40-Ampere-hour (Ah) drain would occur on the battery. To keep the pump operating for 8-hours, however, will most likely require a battery with more than a 40-Ah rating, as the pump likely could not run well when the battery was more than half discharged. That suggests an 80-Ah battery, which typically will weight about 80-lbs in a lead-acid battery. That is not a small battery.
The amount of rain water that can be gather by the open cockpit of a boat and collected in a sump area can be impressive. Does the boat have a mooring cover? If not, a considerable volume of water could be accumulated in the sump and cockpit during three-weeks of rain. If the sump drain cannot be left open, then a battery-operated sump pump would be a must.
If you do decide to install a second battery, I would use a battery that was sufficiently large that it could also serve to start the outboard engine in the event the dedicated cranking battery cannot. I would re-wire the boat electrical system so that all electronics and other house loads were connected to the second battery, and the first battery was for engine-starting service only. I would add some circuitry to permit the engine to charge both batteries. If you decide this is the preferred solution to the mooring unattended problem, I will be glad to offer more advice. But first, I think a solution without adding a second battery should be explored.