DESQview did not do any memory management of its own, and it did not use graphics. It was entirely local and had no networking. It was famously fast. It was a DOS multitasker so it managed DOS tasks, meaning multiple slots of 640kB. On a 386 with 4MB of RAM you could have 6 full-size DOS VMs with a bit left over.

If you were a power user you could still have say a big 1-2-3 spreadsheet in EMS plus a few DOS VMs.

DESQview delegated memory management to QEMM386, and QEMM386 did not do swapping. It didn't need to.

DESQview/X was a totally different product, with a full GUI, so much bigger and slower -- and it added an optional extension that added full virtual memory with swapping to disk.

I am wondering if you are mixing up DESQview (small, fast, local) with DV/x (big, complicated, networked, had optional VM)?

Or indeed DV/x with something else altogether? OS/2 maybe?

Because if it was swapping, it wasn't DESQview, not in any normal sane config anyway. It might be possible to add DV/x VM to plain old DESQview but I never heard of anyone doing that.