Serial EEPROM with FAT
Yes, it is possible, but you'd need some kind of controller, you couldn't just wire the eeprom directly. This is because the EEPROM does not speak SD card protocol. I would probably bypass SD completely, and just use USB. So something like:

SPI EEPROM &lt;-SPI-&gt; AVR &lt;-USB-&gt; PC


Look into the examples provided with the AVR USB library, Lufa, one of the examples shows exactly the above setup...except it's using an Atmel DataFlash instead of a SPI EEPROM. But it's possible, you'd just need to change the code which accesses the Flash to instead access the EEPROM.