Would organisms genetically descendent from humans fall under the purview of the Catholic defined God?

This idea of propagating the human 'race' through bacteria of other DNA carriers is relatively new even to the fields of science and philosophy and is premised on a very secular humanist world view with it's own existential definitions of things. I do not think any major Christian group¹ currently has doctrinal statements that speak directly to the issue using the same terminology; although that is likely to change in the near future. Most issues raised in the secular world that have spiritual implications are eventually addressed specifically, but usually this is done in response to confusion or errant doctrine. Rarely is it done preemptively.

That being said, it is also not any stretch of the imagination to extrapolate from well established principals and suggest what Christianity's position on this is in general terms.

1. In Christianity across a wide swath of theological spectrums, EVERYTHING is seen as falling under the purview of God. Certainly none of the major branches of Christianity would disagree with this and off the top of my head I cannot even think of any sects that take a radically different view. This is clearly expressed not only in Scripture but in many creeds. For example even in passing, mentions of God often identify him as the God of everything in all of creation.

   Acts 17:24a (ESV)
   ²⁴  The God who made the world and everything in it, being Lord of heaven and earth, […]

   In other words it does not matter what matter you ask, how it is tinkered with in a laboratory, or where it is located, it will be the preview of God. Another expression of this that shows the all-encompassing nature of creation as God's is given in Colossians in relation to Christ (interpretation of this varies in some sects, but the gist of the idea that all creation, not just parts of it belong to God is pretty constant).

   Colossians 1:16-17 (ESV)
   ¹⁶  For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. ¹⁷  And he is before all things, and in him all things hold together.

2. In spite of specific differences in understanding (e.g. bipartite vs. tripartite nature of man, the extent of 'sin nature', etc.) Christianity almost universally recognizes some basic attributes of man that make him human. How there are expressed has adapted to our scientific understanding, but the basics remain unchanged. In some specific attributes humans are distinct from other created beings. It is not the fact that we are a living organism that makes us human, it is the fact that we have certain properties. In official doctrinal statements this will be variously identified as "having a soul" or "being able to reason", but they all stem from man having been made "in the image of God".

   Genesis 1:26 (ESV)
   ²⁶  Then God said, “Let us make man in our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth.”

   This distinction is not made for the creation of other species of animals and I know of no Christian sects that do not recognize at least some basic distinction along these lines.

From those two basic Christian beliefs in can easily be extrapolated that:

• Christianity does not (neither historically nor currently) label anything as human that does not fit the classic understanding of such. No bacteria or disembodied tissue—whatever DNA may be present—is considered a substitute for the combination of body and soul that comprises humanity.

• Under no circumstances, no matter what science comes up with to advance or pervert creation, will any part of the physical universe be outside the the rightful dominion of God. Historically even attempts to suggest otherwise have met with God's blunt denial that such a thing will be (see for example the Tower of Babel episode).

_{¹ A notable exception might be "Christian Scientology", although to my knowledge the branches that have significantly different doctrinal views on issues like this also don't claim affiliation with Christianity in a way that would make them relevant to the scope of the question.}