I just replaced my bilge pump last summer.
Naturally the new pump would not fit onto the old base. But I still filled the old holes with epoxy. I just don't like the thought of holes in the bilge. In the fall I did remember to remove the pump from the base when the boat was pulled out. I put the pump up so it would not sit in antifreeze all winter long. I believe that may have hastened the demise of the old pump. The original pump lasted 9 years.
Just a note, while I was in the store deciding on a new pump because the original manufacturer had been bought out, there was an owner from a Catalina 36, same year as mine, who was also looking for a new bilge pump.
His boat had the same size pump as the Catalina 34.
By the way I did seal the new screw holes just out of habit.
I was impressed with the way Catalina sealed the in line fuse and connections so they would not draw moisture or short out in the event the bilge flooded.