The short answer is not in any guaranteed way, it is even a bit worse in that it offers no way to even provide a unique image ID on export that you can trace back to the image much less an iteration of edits of an image.
You can get close to a unique image ID by renaming on import, and using the Image Number feature, which is mostly unique (i.e. it is an incrementing number, but since it can be reset manually it does not guarantee uniqueness). Even that is master image number, not virtual copies.
If you use the export "sequence number" you have to enter it each time, so it just makes you keep track, which is not very useful. Using the image ID as above will let you at least trace back to a specific image among similar ones, but not among virtual ones, and not at all among specific iterations of export after changes.
Now all that said, this is actually quite easy if you are a plugin author, since internally there are both image ID's and develop preset hashes which together would certainly be unique over any changes (You could even throw in metadata presets if relevant). But in a brief look I did not run into any plugins explicitly aimed at exports that allow that. There are some aimed at metadata manipulation (e.g. Jeffrey Friedl's various ones, a "LR/Transporter" tool as well as "Search Replace Transfer" plugin -- google should find their current homes, not including as they may change around). I did not experiment a lot but I did not see any way to get to where you want to be with their use, but it might be possible, e.g. let export use filename, try to change filename with these tools, but even then I suspect you will need to remember to run it before export.
So again, short answer I am afraid, is no.