Can I use the embedded ST-LINK/V2-1 USB of an STM32 Nucleo board to create a USB mass storage application?
No, most likely you don't want to change that. The USB connector is for the onboard ST-LINK MCU. It runs its own firmware to make it the ST-LINK it is.
It will connect to the target STM32 with SWD/JTAG for programming and debugging purposes. It has just the mass storage interface for programming the target.
So it can't be used for anything else, unless you erase and reprogram the ST-LINK MCU, but then you would lose it being the onboard ST-LINK so programming and debugging would not be possible.