If you purchase any of the beverage packages (Deluxe, Refreshment, or Classic Soda) you get a 17oz plastic souvenir cup from Royal, which you can use on the few Coca-Cola freestyle machines onboard; you don’t need the cup if you want to get a soda from a bar or restaurant, as the package is activated on your account.
You can bring your own cup and ask a bartender to fill it or transfer the mixed drink on it, but you won’t be able to pour soda from the Freestyle machine.
Personally, I like stainless steel cups because they help avoid sweaty cups and ice melting, which happens a lot when you get your drink served in royal’s glasses, because popular bars are so crowded that glasses come directly from the dishwasher (hot) and the ice used melts fast.
I always bring my own tumbler, and while it may seem like a hassle to carry it around, when I don’t have it with me I’m always end up needing it.