If you are talking about a through- bolt, where the water followed the bolt down the top and out the bottom, that is good, the water may have not traveled laterally since no head pressure buildup.
To verify core condition, from the bottom, drill a series of 1/8 in. holes shorther than the thickness of the pulpit by 1/4 in, space them say every 2 inches. Put a stop on the bit just in case.
The difference between good, wet, or rotted wood will be apparent, especialy the rotted wood - will be like air instead of wood hence need for bit stop. Whatever comes out of the holes rub in your fingers to see if at the least it is moist. Dry i sdry you will know it. If all is OK, fill te holes with thickened epoxy
It may be easier to do this with the pulpit off and upside down.
If you are in a colder climate you can also sound out the pulpit two times, once when it stays below freezing and another well above it. Wet wood turns to rock when frozen. Same goes for deck - tank covers and the like.
