Yes, when I was a newbie member I had some questions about songs that were not in the DT, and so on.
At the time, Dick Greenberg -- was that his name -- was still living, although ailing.
The Greenbergs had a great deal to do with the DT, and when Dick Greenberg in particular was no longer well enough to continue the maintaining and updating chores, things sort of came to a halt.
That was the gist of what Joe Offer said back then, in answer to the questions I had.

Now Dick Greenberg is no longer alive;
and at this point the whole DT database and its upkeep
are at a transitional stage,
I literally do not know who does what at whose direction nor how it is now done.
Which makes me speculate, maybe it ISN'T done at all with the DT under the present conditions,
and Joe Offer has to sort of work around the DT instead of working with it.
If I'm mistaken, I'm sure Joe will correct what I've said.

So, Mo the caller, in answer to the OP,
No, a Lyr Add thread does not automatically link a lyric to the DT.