Well, I don't know what drilling a hole in the bottom of your boat has to do with winterizing batteries, but to each his own. Me I try to keep the water on the outside and more holes in the hull, below the waterline certainly provides another avenue for water intrusion.
I think the smarter approach is to find out where the intrusion is coming from and stopping it, then buy a $50 wet/dry vac and vacuum the water in the bilge out. The vac can be used for other services as well.
IF you don't like those 2 ideas, occasional visits to your boat will allow you to connect power and run your bilge pump. DO NOT stay connected to any power while in storage.
Now, to winterizing batteries. Wet cells need to have the appropriate amount of water in the cells, be fully charged and checked at least 1 time during the layup period. IF they are 12V batteries, I wouldn't suggest letting them fall lower than 10.5V or so as checked with a voltmeter.
IF they get that low then a charge would be recommended.
Winter cold can have an impact on the charge, but since they aren't being used, all power from them shut off, which I do by turning off my power panel with the 3 position switch and then also shutting off our inverter, then they will last longer. I do NOT disconnect any power connections in our banks.
IF during your inspection you find that the batteries need topping off, charging, I have used a regular car battery charger. Most storage locations will not allow a constant connection to a power source while in storage, but will allow you to connect to power to run a charger to bring your batteries back.
AGM batteries are a different animal. They share the characteristics of a wet cell but there is no water maintenance that is needed or can be performed.
AGM batteries seem to hold their charge much better and that may be due to the number of plates they have internally.
In a side by side experiment, last winter, we were on the hard in Cayuga, 1 of the Finger Lakes, in upstate NY. I have 6-L16 AGM 6V batteries in a house bank and had 2-4D 12V engine, wet cell batteries. Thru out the winter I made 4 trips to our boat. Each visit required me to charge the wet cell batteries. The AGM batteries held their charge all winter with very little degradation. NO connection were removed during this storage.
This winter we are on the hard at Georgian Bay, in Canada. The wet cell engine batteries have been replaced with 2-4D 12V AGM batteries. She was put on the hard the 7th of September and we finished our winterization and left her with batteries fully charged on the 21st. I plan a trip to check the batteries during the Toronto Boat Show, probably around the 22nd of January.
Got my fingers crossed and knocking on wood & my head.