Answer:
I would recommend going to a shorter program in culinary arts to learn the basics and then while you’re getting your other degree, working in the industry to pay your bills, you would be learning the culinary trade further whilst still getting your degree and making money. By the time you’re done with your degree you’ll have enough experience under your belt to get the job in the culinary world that you want, or pursue your career in the degree you've been studying.
With several years of culinary experience, you can leave the cooking world and do something else, but ultimately will have the resume to come back if you choose.
If you wait to do culinary school after your degree, you’ll have student loans, and believe me, a cook job is not going to cover those and the cost of living.
Besides, you’re probably going to need to work while you’re in school anyways, might as well put that towards something that can further your career options in the long run.