I would say your cored hull depth soundings would be erratic, intermittent and inaccurate with a "shoot thru the hull transducer". Typically (in a solid glass hull) it is necessary to have a viscous fluid or dense material between the transducer and bottom. This is usually done by inserting the transducer in a section of 3"-4" dia. pvc pipe, filled with mineral oil, glassed-into the inside surface of the lowest point in the bilge, aft of the keel.
An alternate method involves securing the transducer to the hull using a slow-set
epoxy to avoid air bubbles during curing. Any air spaces or voids within the signal path will affect transmission. Therefore, the cored hull would affect accuracy. You could try filling the cored section beneath the transducer with injected
epoxy resin to increase density.
You will be better served by using a bronze thru-hull. Make sure you remove a 1"-2" section of coremat around the inside perimeter of the hole after boring to minimize water intrusion. Fill with
epoxy before securing the through hull fittings.
Best, Steve