It doesn't. If NICS was defuneded today, and didn't answer a single call, people could still purchase firearms. In most states. Those states they couldn't would have state law at fault, not the NICS laws.
You are arguing for Universal Background Checks, but you are saying the mandatory system would not be mandatory...
How would it be a UBC if it were optional?
"Gee, the system is down today - waived UBCs for everybody!"
I don't think that is how it would work.
Meanwhile, you mentioned that after a certain period, if no response is given by the system, the FFL can still complete the transaction. While this is true, most of them won't, because ATF will expect their assistance in recovering the firearm should the check ultimately come back with a denial.