Correct. All notions are tools constructed by and for human minds for their own purposes. It's possible to hypothesize a definition-breaking example for nearly everything that isn't a mathematical abstract. What counts is useful definitions. In the case of "life" we already have many examples of things that don't perfectly fit the definition, like viruses and prions.
I don't doubt there is some relationship, but that isn't the definition of domain. Otherwise we'd have 1 domain.
> Archaea (/ɑːrˈkiːə/ (listen) ar-KEE-ə; SG: archaeon /ɑːrˈkiːən/ ar-KEE-ən) is a domain of single-celled organisms. These microorganisms lack cell nuclei and are therefore prokaryotes.
The three-domain system divides life in Archaea, Bacteria, and Eukarya. In this system, Archaea and Bacteria can be grouped together as prokaryotes.
In the two-domain system, the division is between Archaea and Bacteria. In this case, eukaryotes are seen as a subgroup of Archaea.
Hope to have cleared up some of the confusion.