Benjamin, I'll tell it to you straight, it won't be easy, it will consume a lot of time, effort, and energy, but if that is something you are passionate about than you can 100% run a business while also taking classes and pursuing a degree. Here's a quick story from my time at college from people I personally know that pertain to your question:
Two freshmen roommates went into school with a dream to one day open up a restaurant. At only 18 years old that dream seemed a long ways away however that never swayed them from. Two months into school it came to their attention that although a restaurant wasn't in the picture yet, there was still things they could've done to get a step closer. The two roommates put their money together and purchased a fryer for their dorm. They started making french fries and selling them to all the students in their residence hall along with drinks and candy. This innovation and perseverance ended up paying off as two years later they opened up their first food truck, and two years after that, their first ever restaurant.
I'm not saying everyone will be as lucky and creative as they were in starting up a business in college, but it is definitely obtainable. Make sure you are managing your time well, being very task-oriented and focused. Don't get discouraged if it doesn't happen right away, because it certainly isn't an easy task to accomplish, but if it is something you want to do, by all means go for it! You will have a plethora of resources at college that can help you learn the fine tuning of a business, there will be a lot of great minds that can help you stay motivated and to constantly learn more and more about the process. I will say, if at any time you feel like the business aspect is getting in the way of your grades and schooling, take a break. You go to college to get an education and a degree, definitely prioritize it that way. Best of luck!