Can quantum mechanics work in a Newtonian geocentric model?

Yes, of course. It does not make any difference whether you have a Newtonian system, an Einsteinian system, or something in between; quantum mechanics is independent of all that. The problem is that general relativity and quantum mechanics do not match up: general relativity is the analysis of all things large, and quantum mechanics the analysis of all things small, and these two analyses do not match up in a lot of ways. Special relativity is going to have issues with quantum mechanics because special relativity does not believe in ether, whereas quantum mechanics is entirely based on a subquantum, Planck-scale ether that fills space. Special relativity says space is filled with nothing, and I do not know how it survived this long; I think because Albert Einstein's name is on it and it saved us from having to believe in a geocentric universe, which is exactly what it was invented to do, as I have proved over and over from Einstein's own statements. General relativity was another story, because special relativity was not working in the real world, which has gravity everywhere, so he invented general relativity to incorporate gravity, and then quantum mechanics comes along and puts a hole in that. Basically, whether it is general relativity, special relativity, or quantum mechanics, they do not really know what is going on; they are like blind men feeling different parts of an elephant and never getting it together.