Can sequence animations be used with particles?
Particles work with materials, so yes, that should be possible. You would really want to test it thoroughly though, I can imagine giving it a performance hit.
As for the foam, i'm not referring to the one that appears when the player hits the water, but also the one when water touches the terrain (e.g: beach).
Foam appears where the water touches the terrain. If the player hits the water, you may see bubbles and splashes; those are defined in the player datablock and are particles.