Edit: To clarify, the following is presented just in case any other users are interested. It is not a complaint or a request, I'm simply reporting my observations.
Unlike HitFilm, the windows version of Action Pro can be run on Linux, using Wine.
As far as I can tell, there are only two problems:
1) The 3d-viewer part of the ui does not display. Bit annoying. But despite this, it is still possible to record the movement of the mouse and add it to the timeline. (I checked by saving the project, then opening it in windows, and the movement is correct)
Edit: ^This was/is a GPU driver issue. I solved it by using the open-source nouveau driver instead of the default Nvidia one
2) The activation app crashes, so it is impossible to activate the software. This means that you cannot save out a .hfcs file, only a .animation file... but since HitFilm itself doesn't run in Wine, you would have to boot to windows or mac to use the .hfcs file anyway, so it doesn't really make a huge amount of difference.
Worth noting that these are almost certainly due to bugs in Wine and not in Action Pro.
But still, good to know.