Can you flatten a clipping mask into a new vector?

You could make a box/shape that is a clone of the clipping mask. Select that object and all the paths you want to clip. Then use the Pathfinder crop tool to remove everything outside the path...

Here is an example result...

Huh. The answer is stunningly simple, and stunningly non-obvious. So non-obvious that I discovered it completely by accident while trying to follow instructions on more complicated ways to do this that involve releasing the clipping group, and then cropping.

Click on the <Clip Group> object to select it. Select no other objects. Then in the pathfinder window, click on the crop button. This produce a regular <Group> (no longer a clipping group) with all the vectors objects inside the old clipping group clipped to the old <Clip Outline>. Essentially exactly what you would expect if you were to flatten the clip group (were such a thing possible). Probably doesn't work so well for images.