Hey EpicFail, welcome on the bladeforums!
A lot depends on the steels used to forge the damascus. Are any of the steels used not stainless? If so, rust is more likely. But just as likely as any other non stainless knife can rust.
Take normal care of your knives and rust should not be a problem.
Wash them after contact with aggressive media and dry them off after washing.
You could use a minerail oil to inhibit rust, you also won't have any trouble with oil contamination then.