Re: First wet slip nerves..
As said above, "Unless you have major dewatering systems, a bilge pump (or pumps) is not going to keep a boat afloat in the even of a holing, unless the inflow of water can be stopped. "
Boats sink from 1. being filled up from the bottom (hole); 2. filled up from the top (rain) and 3. filled up from the side (swamped).
According to the info above, which sounds impressive and reliable, the bilge pump isn't going to save the boat from a hole: bellows tear, plug out, through-hull or sea **** failure. They will, however, do this: cover a small leak, buy some time (boat needs to be attended) and warn others (neighbor/marina staff sees pump running).
As for rain: an operating bilge pump can handle a rain storm, even at the reduced capacity of 10 GPM. In fact, most boats can survive most single rainstorms if the pump fails (they won't be in the water for a hurricane). The sunken boats you see after a single rainstorm were usually already holding water, or were taken down by #3. What the boat can't handle, is multiple rain storms that first, wear out the battery and second, accumulate water in the bilge.
It's not an issue on a self-bailing boat IF the boat is attended: someone would notice water accumulating from clogged drains. So this would be an issue for a boat out of sight for a week or more; not for one at a tended marina. For many such boats, very little water gets into the bilge from the floor-but that is where the bilge pump is, so water accumulated top-side is not addressed by the pumps no matter how good, big, or many.
#3 is the boat killer, how well I know. This is where the good information posted above is so important. Focusing on a boat at a slip, here's how it happens: a. in an OB, water from wave action coming in over the low spot in the transom. Couple that with accumulated rain and it's a goner. The pumps can't keep up. I've seen that happen when a boat is tied with the stern into the wind, when the wind and waves kick up. A good reason to back into a slip. b. stern anchored against current--not frequently an issue in a slip. c. some part, even a small part, of the boat caught under or on the pier. This is huge for us tidal boaters. literally a half inch snag can kill a 20' boat. Even if the splash rail hangs on the pier, that can lower the opposite corner, or motor well, enough for it to ship water.
Look for the lowest water entry point: usually the transom, but maybe a vent or open through hull, or gap under a rail. That's the Achilles heel.
So No. 1 Big Hole is unstoppable; small leak managable; No. 2 one rain between visits is no problem, multiple rains might be; No. 3 the big killer, prevented by mooring technique, not pumps.