Thank you both MichelBParis and @R_Kelly! Seems that R_Kelly strictly speaking is right, however @MichelBParis is right too 
. Forgive me also if I upvote my own answer, but I think it will be useful for others who have the same question.
In short:
One can utilize the Camera Raw bundled with PS Elements,
as if it were near-native to Bridge (read below for the caveats)
allow me to elaborate:
- The Adobe Camera Raw included with PSE seems to be a separate instance from the CC one (probably resides in a different folder too)
- From within the PSE Editor, opening a RAW file will bring you the ACR dialog (of course simplified, without the spot removal/masks and split toning that come with the full CC version)
- From withing Bridge, pressing on Open in Camera Raw... shows the message "Camera Raw editing is not enabled" that @R_Kelly mentioned
- However, from within Bridge if you press on Open With -> Adobe Photoshop Elements 15 Editor, it will in fact launch ACR (PSE's version, after first launching PSE), at which point you have the opportunity to work on the RAW just as before, and either press Done (or Cancel) and return to Bridge, or press Open Image and have the image open further in PSE.
On the bright side,
- Bridge can without any issue send multiple files to PSE's ACR (which helps a bit with batch editing)
- Bridge seems to be reading the new/updated XMP files just fine as if it were "its own"
- the previews generated are accurate
- there is also the icon indicating that this particular raw file, has applied adjustments on it
- the thumbnail refresh instantly as if they were made with its own version of ACR (the full CC ACR)
- inside ACR you can re-edit edit adjustments that were previously created by the full CC ACR version and
- interestingly enough the adjustments that are not supported here (like spots removed, perspective correction etc) will remain, albeit no longer editable.
- However if you click "reset camera raw defaults", these adjustments will be discarded as well!
Major caveats,
- you can no longer use the Develop Settings -> Camera Raw Defaults/Previous Conversion/Clear Settings from within Bridge, so you have to do it from within ACR which means that for batch editing, there are a few extra steps involved.
- you loose access to good tools such as the spot removal tool, split toning, perspective correction, dehaze and of course masks (as seen here)
Other minor caveats that I've discovered are
- you may end up keeping a copy of PSE always open since it needs to have been launched before ACR launches (unlike the CC version that can launch directly from Bridge)
- another implication of that is that while in ACR when you click Done or Cancel, the ACR window will close, but not the PSE Editor window
- The Open in Camera Raw...context menu (just like the Develop Settings mentioned above) inside Bridge doesn't do anything useful anymore - instead you have to click on Open With -> Adobe Photoshop Elements 15 Editor which is a bit more cumbersome thanks to the one extra click, and having to scan for it in a bigger list (if you have multiple photo-editing applications installed).
All in all, it's quite usable even though not directly supported.
Background (how I tested it):
on my system I have Bridge CC 2017 and Photoshop CC 2017, but the Photoshop trial has already expired. Since then, whenever I would choose from within Bridge the Open in Camera Raw... option, I'd get the message that @R_Kelly has mentioned.
- After downloading, installing and launching at least once ACR from within PSE 15's trial version, I tested Bridge again but again no luck.
The PSE trial that I downloaded had ACR 9.7 (or was it 9.6?). From within the program I was given the option to download a newer version of PSE and ACR 9.8, which happens to be the same version that Bridge CC 2017 contains; so I thought I could try that too. This hinted that CC and PSE had their own separate copy of ACR that needs separate updating. I installed the update, but no luck with getting Bridge to integrate with that version either.
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