Yes, as long as the sheet rock is in good stable condition. Water stains will need sealing with a stain resistant primer. Oil base Kilz or a tinted shellac will work the best. Apply 2 coats of primer before the paint.
How do you know if water stained sheet needs to be replaced? How do you know if the material behind it is damaged from the rain/snow that caused the water stained sheet rock needs to be replaced (installation)?
Several ways to tell;
1- If you gouge at the surface the sheet rock will be very crumbly and fall apart. Use a corner of a stiff putty knife or 5-way.
2- Severe damage could bow from the surface. Mostly applies to large areas.
3- The surface paper could be bubbled or easily pulled away from the rock surface.