No. Normal water-based paint will not get rid of those. That's the knots bleeding through.
Knotting solution or oil-based aluminium wood primer can be applied over those.
Water-based Sadolin Superdec is supposed to cover knots - but success is limited in my experience.
You are supposed to sand back to bare wood before applying treatment over knots - but I have had success just sanding the paint as normal and applying knotting solution with going back to bare wood, but whatever you don't tell anyone here.
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