It won't, I'm afraid. The Camera: Shake Action can only affect AC cameras - not a third-party one.
UFPS's camera-shaking effect takes a different approach with its own Earthquake etc scripts - see this thread, for example. If you are able to write a custom script on your UFPS player that invokes an earthquake effect, you can call that script's function using the Object: Send message Action.
Alternatively, you could try animating the shake manually with an Animator in your UFPS rig (not the root object), and triggering the animation with the Object: Animate Action.
Comments
UFPS's camera-shaking effect takes a different approach with its own Earthquake etc scripts - see this thread, for example. If you are able to write a custom script on your UFPS player that invokes an earthquake effect, you can call that script's function using the Object: Send message Action.
Alternatively, you could try animating the shake manually with an Animator in your UFPS rig (not the root object), and triggering the animation with the Object: Animate Action.