Yes, just take light cuts. You can also stabilize with thin CA as your turn. And if you want to, there are several places you can send it to, to be stabilized.
I recommend a CA finish, however. It raises splinters easily (sort of like wenge) and the CA keeps them plastered down better than a friction finish. It also dyes well.
Cypress goes from square blank to pen size in the blink of an eye. It will also grab a tube with CA applied unlike any wood I have turned. I finally went to Gorilla Glue after getting several tubes stuck half way inserted.