Unfortunately you wouldn't have any guarantees on the output of any particular image though, just some reassurances about the expected behaviour over the training set.
You don't have any guarantees with this non-convex optimization.
I think most of these methods would work OK on out-of-domain data.
(Lossy) neural compression methods may also synthesize small portions of an image to avoid compression artefacts associated with standard image codecs, so should definitely not be used in sensitive applications where small details can make a big difference such as security imaging, guarantees or none.
Unrelated, but I actually recognize your name from Github - I guess deep image compression is a pretty small space.