Hi Jan, the answer is YES and NO :-) I'm using a GoPro with Camtasia, and here's my workflow and some experiences. Perhaps this helps you make a decision.
So the GoPros do not function as webcams. This means you're going to have to record the GoPro footage onto SD card separately while recording the screen (and probably your voice). That's what I do, and it works fine. You just import your footage, sync it up, turn off the GoPro's audio volume and start editing.
Now in theory, once synced up, your footage *should* stay in sync. In practice however, that's not always the case. I did a lot of experimenting, and the snag seems to be that the GoPro and Camtasia need to record at the same frame rate. You'd think 30 fps would be the solution - it's available in Camtasia Recorder as well as on the GoPro. But as it turns out, the GoPro records in 29.98 fps and it seems to upset Camtasia. Footage that's synced up at the beginning of the sequence is out by a couple of frames 5 minutes in.
The solution (at least for me) is to record both the screen and the GoPro at 25 fps. That keeps things in sync for longer - if you never make an edit. If you edit and cut bits out of your footage (which inevitably you do), Camtasia seems to shift the GoPro footage ever so slightly - which means that after 5 or so edits, you may need to re-sync the footage. It's no biggie, but it's one of those bug fixes you wish they'd address at some point. Well perhaps they don't know about it.
I've been using this setup with a GoPro HERO 4 and Camtasia 3 on both my Mac and Windows systems. Works a treat. Picture quality is excellent when you go full screen, there's less load on your system to record the video, and Camtasia handles it all very well (aside from those pesky sync issues).