Is there any way to match cuts (both placement and duration) to another video?

I think the simplest way to do this is to duplicate your video layer, then select all the video layers(CTRL + A).  Holding ALT, drag the smoke layer onto the timeline.  This will replace all the video layers with smoke layers, but retain the cuts. 

If you are working with a 15-minute video that has a smoke overlay, the easiest way to accomplish what you want to do is to render a seamless loop smoke video that is long enough to cover your longest cut, plus about 5 or 10 seconds, then move over to Premiere Pro to finish the edit.

Drop your edited 15-minute video into Premiere Pro and import your rendered long smoke video. Drag it to the sequence above the edited video, and set the blend mode to screen if the smoke video does not have an alpha channel. Now, all you have to do is copy and paste the smoke video in the sequence and start lining up the cuts. Just make them have random start or end times. If you use the Q and W keys with the smoke layer selected, the Q will trim the start of the smoke layer to the Current Time, and the W will trim the out point to the Current Time. You should be able to put the thing together in just a few minutes. Monkeying with a script to detect edits and then trying to shift in and out points of a long looping smoke clip is going to take hours, if it is even possible. 

It is a terrible idea to string together more than one or two shots in After Effects, and you do not need any of the After Effects tools to add a smoke layer to some footage.