Yes, this is possible. If you use AT28C256, for instance, you will have EEPROM storage of 32KBytes. Address it as you would address a static RAM, means choose 'memory mapping', where !RD and !WR lines are used to control the read and write sequences.

AT28C256, and similar types, have a nice feature: 'Software write protection', which makes data losses during brown-out events extremly unprobable.

One point, which must not be forgotten is, that EEPROMs need several milliseconds to perform a write sequence (burn period). If this is lasting too long for your application, then a static CMOS RAM with battery backup should be used. At Dallas website you will find modules already containing SRAM and battery. A bit expensive, though...

Kai