In theory, sure. Sounds like a pain to me, though. Here are my concerns:
1) Any water treatment is partly dictated by the grains in your mash. Are you sure your c60 is evenly distributed between the two tuns?
2) Runoff one cooler, add sparge water, Runoff second cooler, add sparge, Runoff first sparge, Runoff second sparge, stop when you get to preboil volume. That just sounds like a three stooges act to me.
3) More stuff to clean. I hate cleaning out one tun, so two sounds like a huge pain.