Yes, it probably can and does. Problem is that the metals are most likely already in their fully oxidized state, that is, with a positive charge, as this is what makes them soluble in water and easily absorbed by your body. And you’re still going to be drinking them. Now if you could reduce the metals (add electrons, opposite of oxidation) you might get them to precipitate out of solution. But then you’d have to have a way of getting rid of small metal particles (droplets, in the case of mercury). Maybe if you could spin a nalgene bottle overhead at a few thousand rpm . . .
Unfortunately, adsorptive filtration (w/ a carbon element) is probably the only way to remove those pesky heavy metals. There’s nothing you could add to your water to remove them.
