Is there any danger that the person gone overboard can be submerged by water during the rescue process?

Yes, if the rescue process is carried out too quickly.

For better speed control, we therefore recommend that you perform rescue manoeuvres with the engine running, rather than using the sails. 

During the return process, drive your ship just as quickly as during your berthing and cast off manoeuvres in the port (1 knot). If you are still unsure, manually drag the person gone overboard nearer to the ship (through the pulley) and use the sea anchor only for the lift back on board.