Sandwich with soaked, wet core is not spongy. Delaminated, rotted core may be spongy or may not, depending on the fiberglass thickness and other supports of the area. Same with taping. Taping can find delaminated, rotted, hollow spots, however it doesn't show wet or dry core.
Technically speaking, core may be delaminated but still dry. It is often a case with foam core in high stress areas. Taping wll sound dull in such areas, however misture meter will show dry area. Opposite is often true too - balsa core can be wet but still structurally sound.
s/v NEMO - Freedom 28 Cat Ketch, centerboard