I've used sharpie to detail sets before. It's not ideal, paint is generally best, but sometimes paint's not practical. (Also, permanent markers are not all the same, if you do use one, use a fabric marker)
One thing I would ask is how you are drawing it. If you have a backdrop suspended from a fly loft, drawing on it with sharpie is going to be hard, because the fabric has a bit of give to it. Paint will be easier.
(Paint is also less expensive)