Could needing an oil change cause the “Service Engine Soon” light to come on?

I have a 2000 Saturn SL2 and I’ve had it for about 2 years now. I bought it used from a good car dealerships. I have never had any issues with the car except a bad windshield wiper arm, that was fixed. I recently got the car fully tuned up in february. I was supposed to get an oil change at 160,300 miles, but I couldn’t afford that change until now. I’m now at 170,280 miles. Could this over lack of an oil change have caused my “service engine soon” light to come on? And would it be anything MAJOR if it was just the “service engine soon” light and not the “check engine” light? I’m REALLY worried and starting to stress and I called a mechanic, who I’m waiting for a call back now. Thanks!

More: Safe (to the vehicle) to drive the car to the repair shop without a rotor? I feel so dumb for buying a 400 dollar car? Any damage to sudden braking at 40mph? How long do I need to wait before taking the road test? I've been driving for about a month, but I'm 22 so I don't have to wait.I'm just not? Steering Wheel Shakes Over 60 MPH after fixing bent car rim. What can I do?