Just to be clear, you want to remove all the water from your soup? In other words, you want to make dehydrated soup powder, or a solid disk of dehydrated soup crust, out of your homemade soup?
The way I understand rice-cookers to work is they shut off as the temperature begins to climb above that of boiling water. Pretty sure that the temperature at the bottom of your soup would begin to climb above the shut-off level before the point where absolutely all water was removed from the rest of the pot. Judging from what happens on the stovetop when you burn your soup, it heats unevenly, and the bottom scorches while there is still plenty of liquid on top.
Even when your rice-cooker cooks rice, it doesn't remove all the water from the rice. So perhaps if you started with soup, the rice-cooker might possibly make a pretty good condensed soup concentrate (?). ...On the other hand I wouldn't count on it.