It will not stun Arm units. The stun lasts for about 30 seconds, give or take a few, and lasts less on pop-up weaponry such as the Toaster. It hardly even effects anti-nuke silos. The stun causes factories to stop nanolathing. The missle doesn't track, or take effect until about 3 seconds after it explodes.
Stunned units regain mobility one at a time, one after the other.
Now let's concentrate on some of the strategies for the Stunner. The first one that comes to my mind is using it to stun hordes of Pulverizers and Cobras so you can safely bring in the Brawlers and Phoenixes. I would also use it to stun the big boy, Krogoth. This is, of course, only possible if you have enough Stunner missles. Therefore, in a large assault I would say it would be safe to save your missles rather than use one at a time, and wait for the next to build.