SPI Library for Microwire

Can I use the SPI library to interface with a microwire eeprom?

Yes.

http://leyenda2.demon.co.uk/mike/Electronics/datasheets/SPIvsMicrowire.pdf

Can I use the SPI library to interface with a microwire eeprom?

That just might depend on the particular microwire EEPROM, I would think.