I assume a fixture save is for repeat work or multiple piece work so that stock positioning is taken out of the equation?
Actually, stock positioning would be more important, as it needs to align perfectly with the previously saved fixture location.
If you're going to use the same offsets (fixture location) for multiple sessions of Mach3, you need accurate home switches, and a method to mount the workpiece in exactly the same location every time.
The offsets are relative to the home position, so you must be able to home the machine to the exact same position each time you start Mach3.
Does it make sense to do a fixture save, just in case, when starting a new project so that you can start where you left off in case something were to happen before the job finishes?
Either that, or just write down the offset values and re-enter them. But again, this assumes you can accurately re-home to a repeatable position.
Is it possible to start a project that you quit if you didn't do a fixture save?
Yes, if you can zero your axis to the sane place you zeroed them the first time.
On my router, I have fences mounted at X zero and Y zero (in machine coordinates) and keep my G54 offsets at zero. All I ever do, is home the machine, place the workpiece against the fences, and start cutting. I never have to set or save offsets.
With one exception. I have a fixture for holding material vertically, and I use my G55 offsets (which are saved) for work mounted to the fixture. So again, I just have to start Mach3, home the machine, and it's ready to go. All my g-code that I use with the fixture has the G55 in it to automatically use the correct offset.