The carryover from one activity to another is generally better the more similar the activities are. In sports, this is know as the Specificity Principle which states:
exercising a (...) particular skill primarily develops that (...) skill.
So to get better at one thing, you should preferably do that exact thing.
That doesn't mean that you won't benefit from similar activities, though. Generally, the more similar the activity is, the greater the carryover. Do keep in mind though, that similar activities put similar strain on similar structures, so they can actually be harmful.
Now to answer your question, is writing with your weak hand similar to spin poi moves with your weak hand? As far as I understood spin poi, not really. Writing is slow and deliberate and you're holding the pen in your hand in a fixed position. This is significantly different to spin poi with its dynamic motions and frequent finger twirling, so at least mechanically there's practically no benefit I can think of.
Neurologically, though, both activities may activate similar parts of your brain, which could mean that there's at least a neurological carryover. But that's not somethingAlthough I candoubt it, as spin poi is about coordination of both hands (even arms) at once, while writing is about coordination of the muscles in one hand. Anyway, I'm not near smart enough to answer that question, so I guess the jury's still out on that one.