Yes, they can supply power concurrently.

For Solarbank 2 E1600 Pro:

When the grid is powered: The maximum total power of photovoltaic power supply and battery discharge is 800 W. That is, the maximum power that the photovoltaic panels and battery can provide to on-grid and off-grid sockets is 800 W in total. More specifically, the on-grid socket can output up to 800 W (from the photovoltaic panels and battery), and the off-grid socket can output up to 1,000 W (where the photovoltaic panels and battery can output up to 800 W, and the deficient output is supplemented by the grid).

When the grid is not powered: The on-grid socket outputs nothing, and the off-grid socket can output up to 1,000 W (from the photovoltaic panels and battery).

For Solarbank 2 E1600 Plus:

When the grid is powered: The maximum total power of photovoltaic power supply and battery discharge is 800 W. The on-grid socket can output up to 800 W (from the photovoltaic panels and battery).

When the grid is not powered: The on-grid socket outputs nothing, but the photovoltaic panels can charge the battery.