If your fuel injectors are only partially clogged or you're noticing engine hesitation then adding a bottle of STP gas treatment and fuel injector cleaner to your gas tank when you fill up can help clean the fuel injectors and make your car run much smoother.
I use STP Fuel Injector cleaner in my gasoline tanks on both my car and truck and use the STP gas treatment fuel injector cleaner every other gas tank fill up.
I've noticed a difference in engine performance and my gas mileage improves by at least 20 miles per tank of gas.
If your fuel injectors are fully clogged then you'll need to either have the fuel injectors replaced or have a shop clean the fuel injectors professionally to remove the full clog.
But if you use STP or other fuel injector cleaners before the fuel injectors get too clogged then yes the fuel injectors will be cleaned up when the fuel passes through the fuel injectors.