If my library doesn't have something that I want on overdrive, I always use the feature to request it. I'd say that at least half the time, maybe more, they end up getting what I requested and it is automatically checked out to me.
My sister is a librarian and is in charge of ordering books for the library. She said when she gets a request she almost always buys the book, since she already knows there is at least one patron who wants to read it. Otherwise, she's basically just making estimated guesses on what will be interesting to people. So always make requests when you can.