Does EEPROM persist after device OS update?

If we save things with EEPROM and then update the device firmware, will the EEPROM data still be available?

Yes, EEPROM data will be unaffected by a application and/or device OS update.

The memory map of the device you use will show that EEPROM not located within the memory blocks where firmware modules reside
https://docs.particle.io/datasheets/boron/boron-datasheet/#memory-map
https://docs.particle.io/datasheets/wi-fi/photon-datasheet/#memory-map-common-