I'm guessing the easiest way to know if the injector is working would be to try to start it. If it starts, the injector is working.
If it doesn't start, turn the key on. You should hear the fuel pump run until the system is up to pressure.
Then, with the key still on, use the kick starter to turn the engine crankshaft. If the injector is working, several times per revolution it will inject a little fuel. When it does, the fuel pump will temporarily run for a second or so to replace the injected fuel.
Just because the fuel injector is operating and the pump is running doesn't mean all is well.
My BMW K-75, a fuel injected triple ran fine for a long time and then developed missfires and pauses when I opened the throttle. I had been running some low cost fuel to save a buck and this fuel didn't have any detergents in it to keep the fuel injector nozzles clean.
After pouring 1/4 bottle of Chevron Techron into the tank and riding the motorcycle, the engine returned to its former smooth, powerful self.