Can you run DOS 16 bit architecture software on a MAC?

By DOS I assume you mean Windows .exe programs, and yes they can under certain conditions.

If you have a program like parallels, boot camp or fusion, you can run Windows on the Mac.

if you want to stay in the mac environment, you can use applications like crossover to run them.

being completely honest, if you want to run Windows applications, just buy a Windows computer, most desktops can be built for less than 400 dollars if you find the right stuff. That and I like my mac to be my fun machine, not Windows machine.