I'd like to see this applied to puzzles with unique pieces like the ones here (https://libertypuzzles.com/about)
Although, from a computer perspective it also makes the edge comparisons nice and clean.
At best, it's crass and tasteless. At worst, it's openly disrespectful and hostile to women. There are millions (billions) of images on the Internet that are available for use under a permissive license - it doesn't take a lot of effort to use something else.
It is NOT a nude image. It might be a cropped version of a what originally was a nude image, but that doesn't make it a nude image. If i crop you out of a picture, its no longer a picture of you? Now it is just a woman with a hat and a shoulder that is not covered with some fabric. If mentally you instantly see the original picture, perhaps you have 'stared' too long at that playboy issue.
Though the point others make in this thread, i think is very valid, it is not a jigsaw puzzle. I was expecting software for when i visit my mom (who likes making jigsaw puzzles), quickly snap a picture on my phone of the table with all the pieces and it would assist me in solving it while she leaves the table for a bit to make tea/coffee. (leaving mom flabbergasted with: how did you...)
To respond to your point - while you might be technically correct in that the Lena image commonly used today is not a "nude" image per se... are you genuinely saying that you don't understand why some people don't like it - or why it's unpleasant and/or degrading to women in the field? Its provenance is well known, and the very association with Playboy (nudity notwithstanding) is likely enough to irritate or upset women in image processing/computer vision circles (I say this having had personal experience of various -- female -- lecturers at my alma mater disagreeing with the use of the Lena image).
Personally, I find it strictly more offensive that people are outraged on behalf of these supposed women, who are so delicate that the use of a heavily cropped playboy image outrages, offends, or discourages them from a field of study. I think regardless of which image you choose, you'll always find some group of people who are offended by it, and anyone who is offended by an image as tame as this one probably has some growing up to do.
If any image is legal as the final picture, I can construct a picture which changes suddenly at the intersection of puzzle pieces. That would be a terrible puzzle in practice, though. You would have to carefully consult the box to see if you had put it together or not. So I suspect for any real jigsaw puzzle, the answer is yes.
That said, reconstruction of shreds is probably possible in most cases, although there is still lots of research to be done in this space. For example the Fraunhofer Society has a project to reconstruct torn documents of the East German StaSi surveillance agency . There seem to be very few detailed publications on their methods, but I did find a high-level overview 
 https://doi.org/10.1007/978-1-4471-4763-3_8 (The Springer page is paywalled, but the DOI can help you find cheaper sources.)