Theoretically yes. I've certain seen copies of Arthur (RISC OS 1 by another name) and RISC OS 2 in EPROM. They only needed 2 x 500K or 1MB ROMS/EPROMS. I'm not sure if they ever made any 16bit wide 2MB EPROMS that RISC OS 3 and 4 needed.
RISC OS 5 is available in one time PROMs.
RISC OS 4 was available in FLASH using chips on a carrier PCB but as they couldn't be flashed in situ (No read/write connected on the 40 pin socket) PROMs were a cheaper/easier solution.