Yes, you can even fence in the slimes in the upper area and put floor there. As long as they have access to water, they will produce slime, which will spawn outside the fence. Very useful if you don't have the ring yet.
Ooh okay wait, but the entire floor isn't covered -- there are spots available next to the rugs etc. Does there have to be a minimum number of spots uncovered for them to produce slimes? I can take away two of the rugs and just leave the center one if that will help.