No, the option to do a boot-time scan will always be available. You can run it at any time. However, it SHOULD only run the one time, then it won't run again until you schedule it to happen again.
It definitely sounds like the boot scan was running. It won't screw your computer up, but it's a nuisance if you don't need it to run.
Again, if you have Spybot S&D installed on your computer, or some other program that prevents changes to the registry, it might be preventing avast from turning the boot-time scan off.
We need to figure out what program is doing it.
So again, do you have Spybot S&D on your computer? Any other security software?