Yes, it's probably cored. You could drill a hole into it to see what the core is. If it's balsa or plywood, the multiple injections can/will work; you have to be sure whether you're trying to re-bond the top to the core or the bottom to the core and drill accordingly. If the core is foam it will be important to know whether the foam is still OK or whether it would rather be dust. If it's dust, or on the way to dust, you should be interested in how much of the boat is built that way. The foam failure will probably be correlated to sun exposure: flat, sun-facing surfaces would be more affected than vertical or shaded surfaces.
I owned a 1968 Flying Dutchman sailboat built by Newport Boats. I bought it in 1993 as a stripped, retired hull. The hull and deck structure was very good when new, but since weight is an issue, it had become non-competitive because of loss of stiffness. By the time I got the boat the urethane foam core was turning to dust so that the face skins would delaminate and fracture under my weight (or the time I hit a rock). I did the necessary localized repairs and kept the boat in use for about 5 years before I gave it away. The hull and deck were about 5/16" thick overall, including about 1/8"+ of foam core.