My expectation, based on no experience whatsoever, is that you will feel the cogging when adjusting the Z screw rotation by hand, and the screw will want to move into specific detent positions rather than being "infinitely" adjustable to the precisely-desired location with the handwheel. But that may turn out to be a "don't care".
The Z screw on my 7x10 looks to be 16 tpi, so that would give a linear distance imparted to the tool of 0.0625" per revolution.
I have never counted them, but my guess is that there will be 200 cogs or detents per revolution on a standard stepper motor. If that is correct, then you would expect to have detents at a regular tool spacing of every .0003125" (plus or minus some slop, because they are not really detents, rather they represent peaks of magnetic attraction).
I suppose that if the screw has detents in its travel, then the workpiece surface might also evidence some associated imperfections, but there's the question of scale and also of other factors that may overshadow any such effect. So, is having detents every 3 tenths along the Z axis going to be noticeable in your finish as you're turning a workpiece? Is the rigidity of the system enough that you would be in danger of having tiny ridges in the surface, or will other mechanical factors make that unnoticeable? Isn't the typical width of the tool face as it makes contact with the surface of the workpiece going to be fatter than that?
My guess is that it's not going to be a problem, but YMMV. You might end up with a surface roughness on the order of a few hundred microinches. But I'm not even sure what kind of surface roughness figures you can expect to get from an unmodified mini lathe - maybe it's comparable to or worse than that figure. You might not even be able to measure that on a DTI. But then I only pretend to be a machinist, so someone who is an actual machinist may chime in and tell me that I'm all wet.
Using a greater diameter handwheel rather than a lesser diameter one might help you to more easily overcome the cogging action...
But as I said, that's just an uninformed guess...