Sure, write a EEPROM load sketch.
You can do it byte by byte, there is library code for that, takes like 3.3mS per byte, or you can load pages at a time, overall would be much quicker.
Depends on the EEPROM you select. I would recommend an ATMEL part to maintain compatibility with the ATMEL uCs.
Try this application note.http://www.atmel.com/dyn/resources/prod_documents/doc8546.pdf
I would write a sketch to capture 2 bytes from ADC, write to 2 bytes of SRAM, do that to capture your sound/spoken number/whatever.
Then write those bytes in blocks to the EEPROM.