Are there DSLR:s (or any other camera for that matter) that embed image stabilisation info in EXIF data? I can't recall I've ever seen that. If not — why not? It seems like a useful marker.
Depending on what exactly you're looking for, yes, at least some cameras do. From my Pentax K-5ii:
exiftool mksm0001.jpg|grep SR SR Result : Stabilized SR Half Press Time : 4.25 s or longer SR Focal Length : 40 mm
Pentax calls its in-body image stabilization system "Shake Reduction" — SR.
These are from the Pentax Makernotes section, not part of the general standard, so results will vary from maker to maker, but the basic answer to your question is yes, there are DSLRs that embed this info in EXIF.