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.
In terms of the decoded image, yes - it's very unlikely you would get something substantially different from the original image. But in terms of the bitrate it's not hard to find examples where the compressed bitrate can be several standard deviations above the average bitrate on the training set - see e.g. the last example here: https://github.com/Justin-Tan/high-fidelity-generative-compr...
(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.
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.