Silk screen layer over pad resist cutouts on pcb
The silk screen is the last step in PCB production. The solder mask is the penultimate step. 

If your silk screen is over (or too near) a pad, that should throw an error from your DRC. Most likely the silk-pad spacing in your DRC settings is greater than the solder mask expansion so you should not have the silk screen going over the edge of the solder mask unless it is too close to the pad (or unless you are doing something special on the solder mask layer such as removing it over a large area for some reason). 

Keep in mind that the registration of the silk screen layer(s) may not be as good as the other layers so you may wish to set conservative DRC rules for the spacing, lest it end up on a pad and affect the soldering. 

If the solder mask cutout is unrelated to a pad, I don't think running it over the edge of the cutout will cause serious problems but it might affect readability if your designators are very small.