Alan, while I am no germ guru, I would say "no." The unit continually receives new tap water ... chlorine and all! The main purpose of the unit is to make that tap water evaporate, and be mixed with the fresh air being supplied to the room.
Inside the unit is a shallow pan, that holds the 'supply' water. This level is controlled by a float and valve, not much different from what you find in a toilet tank.
The pump takes the water, and delivers it to the top of a 'pad.' I've called this pad a sponge, but that's not really correct; the bad does not absorb water at all. Rather, the pad material is more like a scotch-brite pad, or a 'waterproof' straw. As the water cascades down this pad, air is passed over it. This is where the water enters the air.
The holding pan can become an algae farm, especially if the unit is not used very much. Other than a bad smell when the unit does start up, I'm not aware of any particular health risk. In any event, there are productas available to deal with this problem, if it occurs.
The key difference between a swamp cooler, and a "chiller", is that the water is NOT recycled. The water makes a one-way trip through the cooler, and generally isn't in it very long.
