Premiere Pro sequence to Audition. Apply effect to all clips originating from one native video file
Don't apply the effect to the clip. That way lies madness. If all the clips were on the same track then you'd add the effect to that track, but since as you've said the clips are on separate tracks you need to send those tracks to a bus, and then apply the effect to the bus before sending that bus to the master track. 

A bus is like a pre-mix, it's useful for grouping tracks with similar audio or audio that needs to be controlled together, or have the same effect applied, e.g. you might have one for all the dialogue, fx, or music. The ouput of a bus will go to your master track by default, but you could send it to another bus if you want and so on.

To make a new bus:

In the track editor window make sure that the inputs / outputs icon is highlighted



On one of the tracks, set the output to a new bus by clicking on the dropdown for the output (I always feel those arrows point the wrong way, but that's just me. It's the bottom one that says Master by default). Then set the output for all the tracks that have the problem to this bus.



You can also add a bus in the mixer panel.



To add effects to a bus / track

in the track editor window, make sure the fx icon is highlighted (next to the inputs/outputs one).

Click on the triangle in the effects rack for the track and choose your effect from the drop down (your list of effects will look different to mine, mine is full of every free VST plugin that money can't buy).



Similarly you can also do this in your mixer window, the UI is the same: