It can be done however I might suggest working with a sample of the material first and see what effect it has.
Ink running down the threads of the material is the main worry.
Going very lightly with the marker, and I mean very lightly, usually does the trick when the ink runs too much down the threads. You will have to go over it several times very lightly to make it look really good.
With luck you won't have to go to this extreme.
Now paint markers do work much better because the paint is thicker than the ink of something like what the call in the USA a Sharpie or felt tip marker.