Will a car pass emissions with check engine light on?

Yes it can, but it doesn't mean yours will. If your check engine light is on then the car is trying to tell you something is wrong. It turns the light on so you know to go to a mechanic and find out the code which will tell you in a human language what it thinks is wrong. In many newer cars you can find the code out yourself by plugging in a small hand held code reader or even by turn the car of then on three times (without starting it, just move the key to the on position, not start) and the code will display in the dash. Then you just need to google the make and model and code number to find out what is wrong. So find out what your car is trying to tell you then try to fix that, it will certainly increase your chances of passing emissions.