Yes. Eliminate oil production and you essentially get rid of the acne (as long as you wash yourself and keep your pores clean). I had the cystic acne in the 11th grade, went on accutane, went OFF accutane, started getting laid, and had brad pitt skin for a year and a half. Eating things like nuts and greasy foods is very harmful for your skin if you have very oily skin, thus leading to severe cystic acne, the worst kind.
If you have cystic acne, I would suggest the ONLY thing to do, and the BEST thing to do, is accutane. Nothing compares.