The CYBLE-014008-00 module and BLE stack supports only one open connection at a time, whether in peripheral or central mode. So it would not be possible to connect to 7 peripheral devices at the same time. However, the BLE stack is capable of maintaining a connection and simultaneously broadcasting in a non-connectable mode, such as what you might need for iBeacon advertisements. Or, of course, it is also possible to switch between being operating as a GAP central and a broadcasting peripheral at different times.
The EZ-Serial firmware is built on top of the same standard components provided in PSoC Creator, so it has the same capabilities and limitations. It does provide a way to operate in a non-connectable broadcast mode while being connected to another device, but it cannot open a connection to more than one peripheral device at a time.