Yes, it can....
I this app you can specifiy a spacing between the puzzle pieces so that each piece can be routed separately with an endmill (or no spacing if you have a laser or just want to print the pattern for a scroll saw). The one thing you cannot do with an end endmill is take a whole picture and cut that into puzzle pieces as you mention. But you can create a blank assembled from puzzle pieces and e.g. machine a 3d image into it. Or photo-vcarve or laser an image into the assembled pieces. A puzzled inlay would be a challenge but probably possible.
I made a 32-piece puzzle from 16mm maple and it came out quite nice for a first attempt (1/8" endmill and 1/8" ballnose). For such a low resolution toy it is surprisingly "puzzling", maybe due to the 3d-surface. I did machine it with too much negative allowance, though and it came out a bit loose. I don't blame Vectric for their policy. As Adrian mentioned they would have to vet everytime someone posts a link for quality and if it is their business interest. I guess I had hoped my humble app would fly under the radar
Anyway, I will post it somewhere else. It was made for my own purpose and the post meant as a free community service.