Hello Shojiro,
Since the ROM APIs reside on an area different than Flash memory, it should not be possible to erase them after erasing the flash memory.
From figure 2.2.1 Memory mapping, LPC81x UM.
Other point to have into account is that the APIs residing on boot ROM will not require the flash memory to execute commands and routines, instead, they use pointers to certain areas of the boot ROM space.
For example :
From Fig 51. USART driver routines pointer structure.LPC81x UM.
I hope this information helps you.
Best regards, Diego.