Small areas of core can be dried somewhat effectively but you need holes in order to facilitate this and often a heat lamp on the underside. These holes can be tough to patch and hide once the sun and some age hits them. They almost always show back up at some point so often times a lamination covering the fared holes is necessary.
Unfortunately this drying process takes considerable time and is ideally suited for small sections. The OP stated that lots of his deck is wet and I would never attempt a drill & fill on a scale that large. Drill & fill works best for areas of fry delamination that were not caused by moisture. Also if the core has begun to turn to mush there is no point in a drill & fill as the structural properties of the deck have been severely compromised and won't be safely repairable, in my experience, with highly viscous penetrating resins.
If the laminate is just damp, not saturated, then the integrity of the deck is still likely intact once dry. Drilling lots of holes can accomplish this on a small scale but ona large scale you are better to de-skin the boat and replace the core..
I have seen a three X three section of deck that was pinning the moisture meter needle still wet at seven months and that was with about 35 - 40 holes in it. In seven months you can do a lot of deck repairs..
This is an example of what a saturated core looks like during the rotting process. If you look ahead of the chisel you can see how the balsa just turns to mush when you touch it with the chisel. This was a deck penetration under a teak hand rail.
Here's another view of a saturated balsa core. As you can see the balsa actually looks wet and you can physically see the moisture.
One should note that this balsa, even in the present condition, still adhered quite well to both the top and bottom skins, in most places, and required a screw driver to pry this square from the rest of the deck. At some point this would have rotted and failed. Even this wet, the deck was still sounding out with minimal differences in tone so the only way to know was with a moisture meter or core sample. To the untrained ear, without a moisture meter and only a hammer, one might assume this deck was in A1 condition.
This is a good example of why spot soundings and moisture readings should always accompany one another.
This is the adjoining deck section to the photo above with the chisel. As you can see the color of the balsa is telling you how wet it is. If you scrape out this core and compress it between your fingers it drips water like a sponge would. It should be noted that at this stage of rot (early) the core is still tightly bonded to the skins. If this moisture were allowed to continue the color of the balsa would continue to darken and literally rot away leaving no strength.
If you just stop the moisture from getting in you can often sail the boats for many, many more safe years. With new water comes air, with air & water comes rot. Prevent any new water and the majority of air, with good sealed fittings, and you'll do well for a while before needing to re-core the deck. Once rot sets in the only effective fix, IMHO and experience, is new core..
Drying the deck, like a hull, is most often a time + time + time = time equation....
