Short answer is yes. I’m not at edit station but goes something like this:
Select clip that is set with fx. Edit>Copy. Then select all clips except the one you copied. And this is what I can’t remember. Go to Edit>Pastes Effects or Paste Attributes. One of those should offer an option to Paste that Effect to all selected clips. Make sure you look at other option in the Paste dialog.
Sorry for vagueness. I’m at a tire shop having flat fixed.
Unfortunately that doesn't solve your issue. You can copy attributes from one clip to all the others but when you want to make a small adjustment to all of them you will have to delete filters (like compressor) from the clips before copying the newly adjusted filter. Of course, volume and other "non-filter" attributes can be just pasted over the top with no problem. I don't know of any workaround like you are hoping for. Sorry. Maybe someone has a workaround.
I think your best bet is to wait until you're picture locked, then expand audio components, separate by role, then you can create a compound clip of all the dialogue or whatever and drop your compressor on that rather than on the individual clips. It's your best bet to creating an audio bus of sorts for this kind of thing.
Assuming you've got all the audio the levels you need them, export project AUDIO ONLY. Import exported audio back into project in as many different track layers you need to futz with. Wail away at adding/removing/tweaking parameters.