Mmmm, not in my state. The term “No-Fault” is a little misleading, perhaps. Basically it means that everyone is responsible for insurance against the first $10,000 of “special damages” (i.e. medical bills and lost wages) and therefore there is not tort liability (i.e. “fault”) for those causes of action. However, for everything over 10K or for property damages, tort liability (fault) still exists and always has.
No-fault was designed in the 70s to attempt to reduce litigation and claims administration costs. 30 years ago, $10,000 went a lot further and covered a lot more medical costs. These days, pretty much any accident with any bodily injury exceeds no-fault limitations and thus the “fault” system becomes available.
Plus, no-fault never applied to property damages. So there can still be a question about who is responsible for fixing your vehicle that is determined according to fault principles.
Bottom line, it sucks to be hit by an uninsured motorist, even in a no-fault state.