It's worth remembering that velocity and speed are different things, sometimes these can be confused or used interchangeably where they probably shouldn't.
I'd tend to defer to the standard I posted above which, to me, suggests that ADS-B out reports horizontal velocity E-W and N-S separately to vertical rate and altitude. Given it specifically states 'horizontal' then I'd take that as meaning the two-dimensional velocity over ground. To me this makes sense (that you'd transmit the raw data as much as possible with minimal or no processing), and if it's solely GNSS based then that's what you'd expect.
Given the data stream is quite rich (also reporting Z / positional components) it's then trivial for a receiving system to determine and supply the 3-dimensional aircraft velocity in space. IOW yes you could determine the speed + direction (and therefore velocity) in a dive.
However this is the derived velocity in space, which is not necessarily the airspeed of the 'craft, and thus the VNE question might remain unanswered if it weren't for other general data that you could also incorporate. Such data might come from area met reports, or aircraft local to the one in question that may also report IAS/TAS (if the subject craft didn't), but as I see it 'simple' ADS-B out by itself won't actually transmit everything you need to determine if the aircraft exceeded limits.
Once again this is largely from first principles and a quick review of the standard detail I've found, so I'd very much defer to people more experienced in the field than me should an authoritative source arrive.
FP.