Sorry to sound harsh, but if you need to ask on an internet forum if its possible, then you are going to fail if you try it so I would get on the phone to Kentucky Fried Chicken and find alternative employment.
You won't care about your CV if your business takes off to a certain extent where you don't need to fill out another job application in your life.
it's okay.. if you had a brighter future than your part time job many success business man start their own business when they're young.. such Bill Gates, Mark Zuckerberg (the facebook owner).. if you 100% sure about your business, then why not ?