I used to have one of those! Well before I ever knew about Linux, but it was great fun making little stuff in BASIC and playing with actually floppy disks.
You can if you emulate a CPU that does have an MMU. Someone has actually done this to get Linux booting on an Intel 4004. Another one got Linux to boot on a Commodore 64.
They tried running Linux on their ENIAC, but someone accidentally tipped over one of the crates of punch cards which has unfortunately set the project back a few months.