Is cell-free Life possible?
Your updated question, as I said in a comment is much more precise but also describes a biologically and thermodynamically absurd scenario that betrays deep misconceptions about how cells work and what they need to work. Having said that I've realized it has an answer, so I'll give it:


  Would we then consider such a thing a genuine living organism and if so why?


As in every case in science where previously-sharp categories become fuzzier through the discovery or creation of entities that fall in previously-empty intermediate zones, "we" would debate ardently about whether those things should be considered "genuine living organisms" or not. There would be several possible outcomes to these debates:

1) All of the new intermediate entities demonstrate that in the space of characteristics things can have, the old category as previously defined no longer forms a sharp cluster, but a sharp cluster still does exist that is pretty close to that old category; in that case the old category gets a new definition, and as a result some entities might change their classifications, or not. Real-world example of this kind of definition change (though not necessarily caused by the appearance of intermediate steps): how stars and planets went from their antique definitions of "stays put in the sky vs moves around" to their current very-different definitions.

2) The new entities demonstrate that what was thought to be a sharp cluster in the space of characteristics is just... not. A clear, universal, unambiguous definition is thus impossible. One possibility is that the cluster dissolves entirely; the category as a whole is thus abandoned (many abandoned taxonomic terms can be seen as examples of this).

3) The old sharp boundaries no longer exist, but there is still a definite cluster in the space of characteristics that can be pointed to, it just has fuzzy borders. Like colors, which blend into each other but we still know there is "red" and "blue" and they're not the same. In that case, like with colors we might abandon the edge and focus instead on doing like we do with colors; defining the entity by looking at what "a good representative of this category is" and "what an ambiguous representative of this category is", thus giving a reliable idea of where the cluster is, where it isn't, and where the boundary is, even if it's fuzzy.

4) Sometimes you do need sharp definitions though, especially in science. In that case there are two possibilities:

4a) Use different definitions in different contexts, depending on which characteristics of the cluster interest us at any given point. "Species" is an excellent example of this; a paleontologist, a vertebrate biologist, a plant biologist, and a bacteriologist will use the same word to talk about similar concepts (a grouping of organisms with specific ecological and evolutionary significance), and they will use different criteria to determine what a species is in each case, meaning they have different definitions.

4b) Settle on an arbitrary boundary based on certain criteria that cuts through the fuzziness, with the understanding that it is arbitrary, other criteria would have yielded a slightly different boundary and different classifications for given entities that exist in the fuzzy zone, but it is useful for whatever purpose to have that boundary and thus a boundary will be chosen. Debate might continue a long time over where the boundary is, and potentially involve different people using different boundaries as in 4a, or not. Classic recent example is the definition of planet, and the process that led Pluto to no longer be considered one. This can also involve the creation of new categories, like "dwarf planet" in the case of the redefinition of "planet".

So to answer your question "would this be considered genuine life?", the answer will be "yes", "no", "it depends" or "neither" depending on which of those outcomes the debate ends up settling on. And we cannot know which outcome it will be, because the choice that will be made will entirely depend on what the space of characteristics will be like that makes a currently-sharp boundary fuzzy... And obviously we do not already know what the space of characteristics is like because those discoveries or inventions that will prompt us to revisit what we think of as "life" hasn't happened yet ! (well, not the ones you posit. Obviously the definition of "life" itself has already undergone the processes I describe many many times as it got better understood !).

(note I'm not even getting into the vernacular, and whether it will follow scientific usage or not and at what rate if so. It's interesting to note it still in many ways hasn't caught up with (or is just unrelated to) today's biological definition of "life" !)

(I will also add that I cannot posit an outcome even based on the specific scenario you describe, for two reasons: first, the decision would be a communal one made by professionals in the field, and I am a single person and not a professional biologist. Second, the specific scenario you describe already goes against everything we currently know about life, so, yeah.)