No you can not add physics to the particles from the particle emitter. They don't have interaction with anything as far as I know.
So, there are two ways around this, one, careful control of particle emitter properties, rates, angles, timeouts etc.
Secondly you can whip up your own particle system. The use of physics should infact make this a little bit easier.
Edit- Do you want to make water using physics particles? If you search for Quaziblobs you will find one technique that could work with some refinement.