I've got two trees on Ancestry: one only recently public and one that will probably stay private for a while.
When the now-public one was under construction, it was just that, under construction, and I was learning the ropes. Once I felt confident enough and had corrected some newbie errors, I went public - including once being overly enthusiastic and following the wrong leads from several other trees. Going public was several weeks ago, but it's still indexed as a private tree, although it seems people can see it now if they click the right buttons.
The private one is a research tree, full of suppositions, experiments, notes and questions to myself, etc., and even has one deliberately false scenario. The false scenario was setting up a man of the same age with the same name in the same town as a cousin so that I had a place to put him. That way I could research everything about him to determine if he was an impediment to linking "my guy" as being my great-grandfather before he came to Canada. Turns out, they were different people.
(That goodness I eliminated the other guy. He married his own daughter's stepdaughter. His son-in-law was also his father-in-law! To make matters worse, the two men had married sisters about 15 years before.

)
I have a note on my great-grandfather's profile on my public tree that research is being conducted on an English family and that that information is in a private tree. The note says that people can send me a message requesting an invitation, but I wanted to make sure that they were aware of the shortcomings of the research tree.
Carol