Nope....the stator is by definition a "generator"(it's usually referred to as that in service manuals and parts fiches), it produces current whenever it is in motion. An alternator(like in a car) can vary output (amps) to match demand. The R/R converts the AC to DC, and limits that output to about 14-15 volts....nothing more.
However in either case, voltage should never be that low. Voltage (volts) and charge (amps) are two different things. An amp meter placed between the bike and battery would show + amps right after startup, assuming everything is working. That would slowly taper off to zero as the battery charges and the system reaches equilibrium. If you shut the motor off but left lights on, it would read -amps. The charging system is still producing it's rated output, but in effect it's being wasted since there's nothing to accept the charge.
Sometimes it helps to define voltage by it's technical term: potential difference. Think of voltage as a difference between two points in a circuit. Not of power, but of potential. 14.5 volts has the potential to charge the battery, but not if the battery is already fully charged. The difference between the charge at the two posts of a battery is unitized in volts. That's why even a totally dead battery can still read 11.5 volts or so. It has potential(volts), but extremely little amps. Think of voltage as the size of the valve, and amperage as the pressure behind it. The valve gives it potential to have a high power flow, but not if there isn't any pressure.
Anyway, a reading of 12.2 volts means your bike is running negative, and if you ran long enough like that the motor would start to run poorly from weak/missing spark, and eventually die on the side of the road. It wouldn't crank, and wouldn't bump-start either. A good fully charged battery should read 12.6, so the bike is consuming more power than it's making. 13.5 is what the Max tends to run at...kind of low, but acceptable. I'd suspect the R/R is no good. Like you said the stator was fine for a while, and those rarely ever go bad....there's really nothing to break.
If you replace it again, get a stator from an R1....better design.