Anyone got experience using a touchpad for a desktop?
Does it relieve stress on the arm?
TLDR: Yes a touchpad will have an effect on your stress if only because you use your muscles differently
Define stress? You mean as in Repetitive strain injury (RSI)?
Well RSI is an overuse injury, but in this cause overuse doesn't mean you shouldn't use your arm. You overuse it in the wrong way for (too) long stretches of time, which is straining for the muscles that control your wrist and hand.
The advantage of a touchpad would be that you have to move your hand more than with a regular mouse to get the job done, which means you don't overuse it the wrong way.
Furthermore, what's bad about most typical mouse usage is that you have to keep your wrist in a slightly dorsiflexed (in this case upwards) position all the time, due to the shape and volume of the mouse.
With a touchpad you could leave your hand lying flat or hold it in whatever position you like, which aids to the less intense use of your overused muscles.
Still, like with most injuries there are other factors that might have an influence such as stress (peer pressure and the like) or lack of coffee breaks (or whatever breaks you like to take), which won't be alleviated by the touchpad. And if you use the keyboard just as frequently as your mouse, using a bad keyboard could still give you some strain.
Disclaimer: using the touchpad the wrong way, i.e. with very tensed finger positions, might actually give you more problems in the long run, so learn to listen to your body!