Three things:
1 Imaging of the plate will need to be a minimum of 2400/2540 dpi
2 Ink/water balance and impression cylinder settings will be critical
3 The substrate you're printing on needs to be able to resolve the text
On a sidebar, even though it's one color job, it might happen that you have to run the text on a second press unit.
You might also ask the printer to run a test using the off-cut/non live image area of a different job.
On a side-sidebar, during my Creo days we would sometimes run 1/2 point text to create ruled lines in marketing brochures. What was written at that size could only be seen/read using a 20x loupe. Lotsa fun.