no to paint you use brush and paint - for that we have verb "malować"
this definition of draw
to make (a picture, image, etc.) by making lines on a surface especially with a pencil, pen, marker, chalk, etc., but not usually with paint
fits perfectly this definition of rysowac
«przedstawiać coś na papierze za pomocą ołówka, kredki»
rysować can also mean scratch and be used as paint in this definition
to describe (someone or something) in a particular way