Can water-based paint be applied to a concrete countertop?
Can you paint it? - Yes. Will you regret painting it? - Probably.
A concrete stain will get into the material and darken it, and then a concrete/stone sealer will reduce the porosity of the surface.
Paint sits on top, and in countertop service will almost certainly get scarred, scraped and generally dinged up - so repainting may be a frequent task. It's not impossible (painted countertops are not unheard of) but it is annoying (painted countertops are not common these days.)