I do not recall ever seeing a headliner thread.  I think it can be done though if the headliner is fairly new.  If not I would be afraid of the thread being deteriorated and having it pull apart when removing.

When I was in high school, I replaced the window gaskets on my 67 mustang coupe during the winter months.  My original headliner was in decent shape but a little dirty from 22 years of use.  I was so proud because got my windows sealed by myself and I saved myself $200.  The first spring day I rolled down my windows, the headliner dropped.  Evidently, installing new gaskets pulled the headliner tighter under the windows.  Evidently, that extra tension and the fact that the thread was deteriorating pulled the headliner apart with the wind.  I learned I should have replaced the headliner the same time I did the window gaskets.