No, because this would open up a way to lock down the knowledge by re-releasing it as (e.g.) copyright all rights reserved.
It might be okay to re-release under a free/libre share-alike license such as CC BY-SA ... but this complicates things (for a start one would need to drop the libre emblem, and successive derived works would have to be exactly CC BY-SA).
So, a "Libre Puro License" would have to be 'copyleftish' (i.e. perpetuate freedoms to have any impact) whereas a Libre Puro Emblem would not (and would probably have a greater impact if it became 'cool').
For a Libre Puro license: people would aspire to produce Libre Puro licensed resources and be assured that the libre nature would be preserved in future derived works. But it is currently difficult to live up to this license and we would be starting from scratch.
To qualify for a Libre Puro emblem all components would need to be appropriately mixed (wrt licenses), comply with the Free Cultural Works/ w:Libre Knowledge definition (the 'Libre Emblem' requires no more than this, Libre Puro requires more: ...), be in free file formats and (where applicable), served via libre services (e.g. via GNU Affero licensed resources), free protocols, etc.. This is easier than meeting the requirements of a Libre Puro License which needs to ensure that the freedoms are perpetuated in derived works.
If I'm reading this correctly, the fundamental difference between a "Libre Puro License" and say CC-BY-SA would be no requirement for attribution under a "Libre Puro License"?
It seems that there is one-way compatibility, i.e. Libre Puro ==> to compatible license, but not the other way around?
You'll need to think about how to resolve the attribution issue. From recollection, the legal code of a CC license through written permission, can remove the requirement for attribution under a CC-License, so the Libre Puro legal code would need to provide for this one-way compatibility.
(I'm speaking under correction here -- so you'll need to check up on this.)