You should have a bilge pump
We have had our Cat 30 over 15 years. It is a 1983 version and came with a bilge pump and float switch. We have the regular shaft packing and always have a bit of water in the bilge, but not enough to cause the pump to run. I tighten the packing when leaving the boat for several months and we return to a dry bilge, however when actively using the boat the packing is loose enough to provide lubrication to the turning shaft, but infrequently drips when the shaft is not turning. We live aboard and observe this continuously. The bilge pump is wired directly to one battery so it is always powered, never switched off. I rarely see a boat without some water in the bilge as sources can be rainwater, refrigerator, spillage, and the usual drip from the shaft packing. You can taste the water to see if it is seawater. There are other alternatives to shaft packing that leave a dry bilge if you so desire. But, I would put in a bilge pump for automatic dewatering of the bilge if I didn't have one.