No it's not. That is ludicrous. If I portray a realistic fight scene, do I make a statement on fights in general? Nope. Replicating things as they are in reality can stir conversation by itself and often that is done with the intend of conveying a message, but it's not a necessity. Nakatani tells a story of a person in that particular situation, but if she wanted to make a statement on lesbians then she completely failed. She barely addresses any lesbian issues aside from some people thinking it's a phase or it being looked at as weird (which is the most basic of all yuri tropes).
If you make a realistic fight scene, it does send some messages to the audience actually. It tells me that you have some knowledge of what real fights look like, it tells me that you wanted to make a realistic fight. I could even infer some things that may not be entirely correct but aren't inconsistent with what I saw. I could infer that you like realistic fight scenes, heck I could even infer that you think realistic fight scenes are superior (I could be wrong in that case but that really isn't the point). Besides gathering author intent is only the least interesting, but still important, part of interpreting a work of art
anyway. Any good work of art leaves room for the audience to interact with it, and Bloom into You is a good work of art.
As an aside I, once again, wasn't saying Nakatani is some scholar of LGBT issues. Yes, the actual LGBT discussion in the manga is pretty bare bones, but I wasn't making a point about that. Literally all I was saying is that it is there.