There really is no rule of thumb that I have observed.
For shows that haven't started previews yet, producers may release availability to TDF if tickets are not selling as expected.
You can look at Telecharge to get an idea of how many seats are left for a particular performance, but that's not foolproof because some unsold seats may be held back for a variety of reasons. If you look on Telecharge, those seats will appear to be sold.
Once a Broadway show opens, you can look at the grosses. The higher the grosses, the less likely it will be on TDF.
Off Broadway it is hard because the grosses aren't made public. In my experience, most Off Broadway shows will appear on TDF. Of course if a show is hot and selling really well, producers don't need to list on TDF.
If a show opens and gets poor reviews, it is more likely to show up on TDF right afterward.
Plays are more likely to show up than musicals.
I would recommend taking a chance on shows on TDF in early previews!