I don't think so, but I don't quite see the point unless you are thinking of using it as a way to archive jpeg's, but in that case there are programs specifically for that, like PackJPG, Lepton etc.
There is also a mode that only preserves the JPEG image data.
The same thing can be done with image data. For something like jpeg you can keep the coefficients but store them in a more compact form.
For what it's worth JPEG XL claims that it's 'reversible', but I'm not sure if that means you get your original jpeg back, byte for byte, or you get an equivalent jpeg back.
I don't think getting the same JPEG is the goal here but getting a JPEG that decodes to the same image data.
But it might be more hassle than it's worth it to create the code and algorithms to do so.
Btw, if memory serves right, Google Photos deliberately gives you back the same pixels but not the same JPEG codestream bits under some circumstances. That's too make it harder to exploit vulnerabilities with carefully crafted files.
If you can't produce the exact same original jpeg, then you can still have some issues during the global upgrade process -- eg your webserver database of image hashes for deduplication has to be reconstructed.
A relatively minor problem to be sure, but afaict if jpegXL does support this (which apparently it does), the upgrade process is really as pain-free as I could imagine. I can't really think of anything more you could ask for out of a new format. Better & backwards+forward compatibility