I am not sure about a possible USB connection between the two devices, but otherwise there simply is no digital connection available. The StudioLive consoles do have an AES port (selectable stereo output signal), but not the rack mixers. The only option is using the XLR and TRS outputs of the 16R.
The 16R has a very good stereo track SD recorder built-in, so with the processing power of Studio One in mind I would think that this is a very nice solution as a "Master Recorder", but it always depends on what is intended and needed to do.
Is the 16R the right audio interface for you? PreSonus has a lot of high quality audio interfaces with variable input configuration (cascading interfaces), which can easily replace a 16R in a studio environment. Compared to the 24R and 32R the 16R as the only single-core mixer in the whole range is very limited. Two effect slots, 16 inputs, six flex mixes, no fixed subgroups - perfect for small live gigs, but probably not for studio work.