No, the S600 has a standard design that is closed when unpressurized.
But there's no problem soaking a seat-saver second stage like the Atomics in the sink. The water may run a few inches up the hose in the sink, but as long as you don't have your first stage below the second, the water won't go anywhere.
I usually just leave my firsts on the counter after rinsing, and soak the second stage in the sink. Let the second stage hang down to dry afterward and you're all set.
Seat savers are fantastic at decreasing the speed with which the seat takes a "set" from the pressure of the orifice. Since the seat lasts so much longer, service intervals are much longer as a result.