IAAP but I'm not so sure what would happen, it's nonobvious. I did find this short article, based on a more thorough research paper from 1997, suggesting it might be possible though:
In short, not only can such a tide-locked planet maintain an
atmosphere, but it might even be habitable over much of its surface,
with an active water cycle and maybe even a near-breathable surface.
http://www.treitel.org/Richard/rass/tidelock01.txt
In short, not only can such a tide-locked planet maintain an atmosphere, but it might even be habitable over much of its surface, with an active water cycle and maybe even a near-breathable surface.