I've never suffered from anxiety nor depression, and yet can't focus on more than one thing at a time. I can't imagine coding while watching tv or listening to an audio book. Nor would I want to!
If I tried doing two things at once, it'd be painful and also I wouldn't be doing either properly. I believe the "multitaskers" aren't that much better, they just learned to context-switch quickly. I'm not the least envious.
"To do two things at once is to do neither"
~Attributed to Confucius, but I first heard it from fortune cookies :^)