There are plenty of versions of Linux that are designed to run in limited spaces, that's not really the point. The eMate has a PCMCIA slot, but I highly doubt that the boot routine in the ROM supports reading an operating system from anything other than the ROM.
Plus, what kind of file system would you format the card with? The Newton only reads one, and that's not really a file system. Certainly not something you could put a Linux kernel on.