[nuccy]

No it is not destructive, math-wise the transformation is bidirectional and can be used many times without any detail losses. The problem is sampling by the image sensor, some pixels endup with larger fiel-of-view than others, so reconstructed flat image of fractions of the fisheye would have different sharpness over the frame.

[Onavo]

So it is destructive in a practical sense. You still need a generative process to fix the "sharpness problems" otherwise you will get a blurred halo after you deconvolve it.