Don't know why you couldn't drill thru the mast plate. You might want to check what's below it as I suspect it might be solid. My boat has a drain hole in the teak/fiberglass directly in front of the mast (about where your arrow is, though at the bottom of the raised step where the mast plate is located). The hole is large enough that I can stick a tooth brush in it to unclog debris. In your photo, the hole behind the mast near the bulkhead was possibly put there for running wires and not necessarily intended as a drain hole. I cannot image that it functions well as a drain
Question, what is the purpose of the turnbuckle shown in your picture?