The benefits of any side project are likely to be unexpected, side benefits. As I was cleaning my apartment I thought of the word nettoyage. Now Racine never uses this word I'm sure, so it only popped into my head because I was thinking in French after reading some things about Racine. So I might learn about the theater in general, about French academic politics, the French language itself, etc... on the side, without any purposiveness.
Now I have to ask myself why I value things with no explicit purpose. It might be because the results of any such activity will not be predictable. That random quality is valuable in and of itself. I also need to prevent intellectual stagnation.
In Juan Goytisolo's memoir, I remember him talking about some college friends, and the topics they were discussing. Goytisolo goes away for a while, and encounters these friends a few years later... and they are discussing the exact same things. JG had moved on, and they were stuck in holding pattern.