I have a global that consists of 1 rich text field and the content is displayed on every page. Does it make sense to cache that? If so, I am assuming it should be cached globally?
It all depends on what your template is doing with the global.
If it's doing something to cause multiple database calls, then yes, you'll probably see some improvement (maybe minuscule, maybe more significant).
Anywhere you use a cache tags brings an overhead of one additional database call, so you just need to make sure it's worth it.