Yes. When I first "graduated" from mom and dad's policy, but didn't have insurance from an employer yet I took out a basic policy with a really high deductible in case of something catastrophic. I paid out of pocket to visit a clinic when I got strep throat, etc.
I didn't have a tv, a stereo, or any furniture (I slept on the floor of my empty apartment)and I had to pinch every penny at the grocery store, but I paid for medical insurance. It was long before cell phones, computers, etc. and vacations wouldn't have even been a consideration. To me, it was considered a necessity and I only would have dropped it if I'd already dropped everything but food, transportation and shelter.
I lived that way for the first nine months on my own until I got acquainted and found roommates. Then things got easier and I had more luxuries.