Yes, but the same insurance company will screw with your coverage depending on your employer.

My mom's plan randomly denied my medications all the time as a student. My current job's plan always provides coverage.

Both were the same insurance company, but she's in a different field with a more stingy employer.

It's especially fun if your employer is in a field with an aging employee population--like higher ed ironically. The insurer gives the same premium rate to all employees, meaning everyone is in the same risk pool. The old and or unhealthy employees make insurance more expensive for everyone at the employer. I've had situations where the exact same insurance plan cost two hugely different amounts of money after switching employers just because of average employee age differences. Really quite perverse.