There is some debate about that. I honestly don't know if the synthetic nute chems kill the microbes, or if its the pH, the lack of food for the microbes, or all of the above. I would suspect that it isn't too good for microbes to try to keep them in a "synthetic" grow without losing most of them at least. I would think that if you start out with a medium and/or additive that has microbes present but then don't feed them anything like molasses, they will die or not propagate to the level that is needed to properly break down the amendments. Then when you add in synthetic nutes on top of that, it may further kill off the microbes that are there which will render the available amendments useless going forward.
I would suspect that if you started out with a solid microbe herd that was well fed and had the amendments available for them to go to work on, they would be able to survive if you then supplemented with smaller amounts of synthetic nutes. The problem with growing in soilless medium with synthetic nutes is that they seem to work best with lower pH, which may kill or shut down the activity of the beneficial microbes. Or if you run the pH higher to accommodate the microbes, it will lock out the synthetic nutes. However, this is more inferential knowledge from stuff that I have read and heard than it is from personal experience. I would cross-reference this with others before taking it as gospel.