It would depend on the kind of job you were seeking with cartoon network, if you specifically wanted to be an animator, probably yes. Though they may have internships to get the experience without the degree to earn a place in there animation department. Sometimes natural skill will take presidence over someone with a degree who has no natural talent. Your best option would be to find an address or phone number for cartoon network and ask what they require. or ask if they have an internship program available for aspiring animators, doing so you may be able to get your foot in the door on this kind of career.