If you want to prove protocols correct, sure, but for someone wanting to move from knowing something about programming to something more, this is not one of the first (20) steps I would recommend.
So, here are a few reasons that recommend learning TLA+:
* If you already know how to program, you can learn it pretty quickly; almost certainly in less than a month. Just use TLC as a highly responsive yet infinitely patient teaching assistant.
* Once you learn TLA+, you’ll not only find it easier to think about systems and algorithms, but you’ll also have more opportunities to practice since you just need pencil and paper. I find myself doodling in TLA+. I'll even go so far as to say that TLA+ has a Tetris Effect[1].
* This is probably true of most esoteric technologies, but since TLA+ is pretty obscure, the community is still in that sweet spot that is the intersection of smart and friendly. Lamport answers questions in the mailing list.
* Just my opinion, but TLA+ (or something very much like it) is part of the future of CS pedagogy.