I'm pretty sure that's incorrect. See page 131 of the manual:
http://files.sma.de/dl/7995/SI5048U-TUS101331.pdf
It's listed as an off-grid inverter.
What the Sunny Island does is serve as a "grid replacement" for grid-tied inverters that would otherwise cease producing power when the grid is dropped.
Let's say you have a Sunny Boy and a nice little 6KW array. When the grid is lost for a power outage, the Sunny Boy shuts down and the system owner has no electricity.
Adding a Sunny Island would allow the Sunny Boy to continue producing power -- it provides a grid-quality reference that the Sunny Boy will use to conform to UL 1741. As long as the Sunny Boy is making enough power to meet the loads, the Sunny Island charges the batteries. When the batteries are full, it changes the output frequency and the Sunny Boy stops producing power and the Sunny Island is supporting the loads from the batteries.
What should become obvious right about now is that you need to have a 6KW inverter for the array, and a second inverter with a large enough output to support the loads. With a grid-interactive inverter (grid-tie: "no batteries", grid-interactive: "grid+batteries", off-grid: "batteries-only"), you size the inverter to the larger of the loads or the array. With the SMA solution, you size the inverters to the total of the two.