I don't believe Tony was saying you wouldn't notice a difference between 1mm and
no nut compensation, but rather referring to .030" vs .040".
Here are some comparisons if you're interested. I calculated based on a 24.9" scale length, with some generic (based on average measurements) saddle compensation figured in. The numbers represent deviation from standard nut and fret spacing, assuming all variables within the setup (most importantly nut and saddle height) were to remain constant. These deviations are all in reference to no nut compensation, but does not imply that as perfect - only using it as a reference.
Here are deviations for a nut compensated .040"

Here they are for a .030" compensated nut.

And here it is for .012"

(numbers are rounded to 1/10¢, so please disregard slight inconsistencies in the progression)
So if you found with your setups a standard layout that your 1st fret was consistently 2¢ sharp and the 2nd and 3rd frets just under 2¢ sharper than your goal, then bringing the nut in .030" would be great. If your upper frets were not at all flat or actually tending to ring sharp however, that .030" nut compensation would be detrimental in those regions. Likewise, if there were no problems with a normal layout by the time you reached the 4th or 5th fret, then the nut compensation could be adding corrections where none were needed. This is why I prefer to compensate the first few frets only, by moving the slots rather than the nut thus leaving the rest of the board unaffected. I should note however that when the nut is cut to what I consider proper height, I find compensating as much as 2¢ in the first frets to be excessive. Fifteen thousandths for the 1st, ten for the 2nd, and five to seven for the third is plenty in my experience.
Now you won't be able to hear a discrepancy of one, two, or even three cents in notes played consecutively. Played concurrently however, it can be enough to be heard in unison or octave intervals, or if they happened to be positioned to do something such as widen a third.
In all practicality though, just build it with what you've got and you'll be fine.