I played Doom like that in win3.11 (which supported disk swapping automatically including for DOS games) on a PC with 4MB RAM while Doom needed 8MB. However, the disk swapping was too slow to make it playable.
I played doom II with 4MB on a 386DX40. We had a DOS 6 boot menu to not load smartdrv. It ran good enough, except on the last level, where all the different enemy types caused all their graphics to be loaded at the same time. That was too much, and caused severe disk trashing (not swapping, DOOM managed the disk on its own).
doom used less memory, so it should have been good enough.
I played doom II with 4MB on a 386DX40. We had a DOS 6 boot menu to not load smartdrv. It ran good enough, except on the last level, where all the different enemy types caused all their graphics to be loaded at the same time. That was too much, and caused severe disk trashing (not swapping, DOOM managed the disk on its own).
doom used less memory, so it should have been good enough.