Jcole--
There is no file system available to the (native) Arduino environment, so in a nutshell the answer is "no". If you need permanent data storage, you will have to use the on-board EEPROM (512 bytes) or add one of the many external storage options (see Arduino Playground - InterfacingWithHardware). Alternatively, concoct a system to transmit data to a PC with a file system (Arduino Playground - InterfacingWithHardware).
Mikal