Yeah DESQview was interesting but you couldn't do everything in it because most serious programs would need all the resources of the computer, or they'd interfere with the IRQ assignments, leading to many crashes.
We're talking a time before even as much as cooperative multitasking of course. DESQview was multitasking programs that were not even meant for it.
Most people I knew didn't use it for that reason. If I really wanted to multitask while BBS'ing I'd just grab my Amiga I had beside the PC (which in itself actually had a real pre-emptive multitasking OS in ROM!).
There were a few programs that could do something else while a download was happening, like Telemate. It gave you at least a text editor and a file manager IIRC.