A surveyor would have told you if you had moisture instrusion and and structural issues w/ transom and hull. So I'm guessing you bought the boat w/o a survey. You probably should worry about a lot of stuff, transom included.
Drilling test holes from the inside of the transom is a way to check things out, but moisture intrusion can be limited to the bracket area, the kicker bracket, the control pass-thru hole, trim tabs, the bilge drainplug. So there are a LOT of potential areas for saturation. Thats why getting a moisture meter reading on the whole thing by a surveyor is probably smarter than just drilling test holes, unless you plan to drill test holes thruout the entire transom. Depending on the condition of the wood, you might be able to let it dry and then fill it w/ epoxy or Git-Rot. But if its in bad shape, you might need to replace the transom.
On my 88 228, I had saturation from the kicker bracket. The center piece of ply was rotted but the 2 outer pieces were ok, so I drilled a bunch of holes, dried it over a 3 month period w/ a low pressure air pump, and then pumped thinned epoxy into it. Took a good qt of epoxy. Bought me some time (5 years at this point, knock on wood)