Here are two relevant links, which say similar things:
The intro to the help article sums up the guidelines and advice that follow it:
The community here tends to vote down overt self-promotion and flag it as spam. Post good, relevant answers, and if some (but not all) happen to be about your product or website, that’s okay. However, you must disclose your affiliation in your answers.
There are two requirements, not all answers should promote one's product and affiliation with the product must be disclosed. The first really only matters once the user posts enough answers; I think in the specific case at hand that it is unlikely that TeX will solve so many problems on this site that too much self-promotion will occur. The second requirement is more important, imho, and the OP has done that. Mr.Wizard summarized all this in a comment on the answer.
The guidelines go on to warn that such posts as these (historically) tend not to be well-received. The guidelines seem to take no stand on this, so I take it that up/down vote wars are part of the give-and-take of commercial self-promotion on a site oriented more toward open-access solutions.
IMHO, which is just an opinion:
That said, why shouldn't Mathematica users be made aware of commercial solutions? That's rhetorical, by which I mean that in general we should. We even have a tag for AceGen, which is not free. On the other hand, I do not think the answer should be voted on without the voter having tested the solution and in some way vetted the product. None of the commentary addresses the quality of the actual proposed solution, and my hunch is that folks are upvoting to counter the downvoting, which would render the voting somewhat meaningless.
Having skimmed the documentation for the product, I'm not particularly impressed. In particular, I didn't see how to configure the TeX engine for
luatex, or some other TeX configuration. There were no illustrations of a Mathematica cell being converted to TeX. Some things are a bit klunky. And so forth. It just doesn't inspire confidence that it would do what I would want to do. But this is just an opinion. I share it to justify somewhat my doubts about the meaningfulness of the voting. The package may run quite well, esp. as you get used to the OP's workflow, idiosyncrasies of the UI notwithstanding.
Finally, it does not seem to be a good answer to the main question, "Can a Mathematica notebook be programmed to work as a LaTeX editor?" I expect a good answer to show how a notebook can be used like any of the popular TeX editors. I'd expect something more like a Wolfram Demonstrations Project notebook with an appropriate toolbar. The software only allows the notebook to be used piecemeal, cell by cell. But that in itself is something worth sharing, again, imo.
In short, in theory, I see no problem with such a Q&A that conforms to the guidelines linked above. I think the question, how to edit TeX in Mma, is one others could answer (although my initial reaction when I saw the title in the question queue was why does everyone want Mathematica to be $Y$ when it's $X$?). This means the Q is asked more broadly than mere self-promotion. And, as I implied, making users aware of commercial solutions, even one's own, seems helpful.