I also done that on a friends' 386SX 25MHz machine that had only 2MB of ram. Doom required at least 4MB (sounds ridiculous as I am typing) and although it used the DOS4GW dos extender that was capable of swapping, it never worked.
On the other side, Win 3.1 was also capable of swapping and ran Doom. It was absolutely unplayable though :)
You know, I still have that 386 in my mom's attic. I'm tempted to break it out and see what it can do.
Ultima VII required a 33MHz 386DX w/ 4Mb of ram, and my computer ran it fine with a boot disk. If memory serves (and I was 7 at the time, so it probably doesn't), a DOS 6.22 bootdisk contained fields for page size, which leads me to believe it had support for virtual memory. That said, I do remember the massive stink that was made about virtual memory when Windows 95 came out, so I could be wrong.
I'm highly tempted to break out that old box and play around with it. This conversation tickles my nostalgia bone.
Doom needed 4mb of free memory. If you had 4mb total, you had to create a boot disk. 8mb machines worked fine without a boot disk.
I also, amazingly, remember running some early version of Pagemaker on that machine. When I went to link text, I would click the mouse to start the process, go get a sandwich, watch some TV and come back 10 minutes later when it finished.