No, you need oil or shellac on water stains. The oil based original Kilz would probably do OK for you, but my first choice is Zinsser Cover Stain. If it's a small area, you can even buy it in spray cans.
Any oil-base primer should seal those stains just fine. (Water-base primer will not seal stains caused by water itself.) Note that the primer probably won't hide the stains, but it will keep them from bleeding through whatever topcoat you apply.