I'm afraid the notion of definition of openness will be at one moment fully 100% connected with, condition by, the conditions and terms under which the "thing" is delivered (published).
So, I would say "yes" for a definition, as the Creative Common or the FSF, trie to give across the choice of their different licenses regarding the notion of "copyleft" or "Free/Libre" or "permissivity", and the notions of rights given:
* one single notion of Openness
* different possible options, making the "thing" openness or not, with different level of openness (or free/libre).
As this OSHWA definitions will be not legal, that means, those OSHWA defintions will integrate a term which indicate that a license will have to match with those definition.
As a consequence, that also could mean, that OSHWA will have to do as the FSF do for its list of licenses, explaining which licenses fit with which definition of openness and its levels.
The point is: FSF has begun to list licenses for non-software things, giving a benchmark of what fit with openness/free/libre notions. If OSHWA do so, will it be aligned with FSF, and what if it is not ? Will it generate a sort of "public war" which will decrease the value of OpenSource Hardware.
If so, that means the definition of Openness for tangible things, should certainty be done across a participative work on progress with free/libre/openness software definition cursor makers (FSF, CC, P2P, ...).
Last but not least, on Single or Option concepts for hardware openness definition: currently, open hardware licenses do not include the software developed, alongside/included in, the work of progress of an open hardware. Or, sometime, this software is part of the hardware. Then, some of us, are currently writing new terms and conditions, or have already contracted, under terms of open hardware licence including a mechanism making the software automaticaly published under terms of listed free/libre/opensource software licenses.
What does it mean, and why to connect this to openness definition for hardware ? That means the definition should clear the fact that an hardware could be made with non-hardware components, and if those components are developed/published under an openness process as fully part of an opensource hardware process development, then those non-hardware components should also be published under openness terms and conditions.
Then, that will have a consequence: as CERN-OHL as TAPR-OHL will have to include software inside their articles, and make a bridge with free/libre/opensource software license by default as this for example:
"When people elaborate, an Hardware Creation made with both software elements and non-software elements, then those software elements are provided under the terms and definitions of one of the GNU-GPL compatible license officially listed by the FSF"
A definition, single, with options or not, with categories or not, will have effects on legal terms and conditions.