In a word, no. There are hundreds of successful entrepreneurs who never attended college and never earned a formal degree. Some of them never even finished high school. In this competitive world, how well you think and create can outweigh any sheepskin on your wall.
Billionaire Billy Joe McCombs abandoned his law school studies to sell cars in the mid 20th century. This didn't stop him from founding Clear Channel Media. Colonel Harlan Sanders didn't even finish elementary school, yet he established a world-famous fried chicken franchise that virtually everybody knows and loves. And speaking of famous food, the founder of Wendy's, Dave Thomas, was a high school dropout who went on to very big things.
20th century industrialist and philanthropist, Andrew Carnegie, never finished high school yet managed to found Bank of America. Tumblr founder, David Karp, was home-schooled and never attended college. World renowned shutterbug, Ansel Adams, didn't complete high school, either, and is considered one of the greatest photographers who ever lived.
If you can't afford to go to college right now, don't worry. Come up with one brilliant idea, put it into action, and you might become a billionaire, too.