Yes and yes, but possibly not. I have seen this error with no network drive involved.
The last time this happened to me I lost the project. I was thinking that the automatic recovery the next time Audacity started might rescue the project. But no, this failed, too and I lost the project. In my case, I was making a simple, but very long recording on a very small machine.
For your current dilemma, I would say just be very very careful. Export what you can. Backup your .AUP3 project file before starting Audacity up again - at least it may give you another chance. There is a recover procedure for corrupt projects here: Corrupt or Otherwise Broken Audacity Project Recovery, although I have never tried to use it for this particular problem.