And yes, the coaxial and composite outputs of your cable box are BOTH simultaneously active.
So you pretty much got it correct. Coaxial out of the cable box connects to the tv, while the composite outputs of the cable box connect to the composite inputs of the solo.
In the connection method above, if both the local tv and slingbox were being watched simulataneously; they would both be watcing the same station and could NOT be independent.
To have independant viewing from the local tv however a slingbox pro hd model would better suit your needs; as it incoporates an internal tuner for both analog and ATSC as well as QAM encoded channels.