Since full text search is working (but still marked experimental by the developers) and several improvements are coming with the next version (no ETA) I can tell you that either an internal note or any other text in all tickets can be found. Had not yet experienced any issues with the search, so yes it's working ;)
Btw. you could also create a new status (e.g. "Closed with solution" or "resolved" or ...) and change the ticket status to that status when closing the ticket. Then use ticket search to find all tickets with that state.
So you can see, there are several ways leading to Rome ;)