No. On the Roland S-1, audio input to the MIX IN jack is sent only to the MIX OUT jack, not to the computer through USB. USB audio output only carries the S-1's internal sound. See "Signal Flow" in the S-1 Owner's Manual for the full signal routing.
To record audio connected to MIX IN into a DAW, connect that audio source to the computer separately, for example through an audio interface.