I have lots of downtime at work, and I'm looking for things that I can do that will, in some way, help me improve my guitar playing overall. Obviously learning theory is a big opportunity, but I've also been thinking about ways I can strengthen my technique -- in particular, my right (picking) hand technique. I'm naturally left handed, and I have always struggled with picking, despite a lot of practice. I decided start practicing writing and other tasks with my right hand while at work, thinking that improving my ability to use my right hand in general would ultimately help my practice efforts when I am actually able to play -- even though the muscle movements involved in picking can be quite different from those involved in writing. Is there any basis to this? Has anyone here ever tried practicing other tasks with their non-dominant hand to improve their playing?
It's not going to make any appreciable difference no.
Only guitar will make you better at guitar.