How about remove the EEPROM from bb white?

I have already follow boot the bone.
I find there is an eeprom on the board, after some search, I got it stores bb’s info.
I wander whether the kernel can boot up correctly if I remove this EEPROM?
If cant, where to patch the kernel to boot it up?

It cannot. You would need to modify UBoot to ignore the EEPROM.