Giggle….we used to have an old Ford pickup that had dropped a valve and put a hole through one of the six cylinders. It was used as a trash truck to go to the dump about twice a month. So long as you kept oil in it and didn't mind fogging the skeeters on the way, it went down the road.
Later on, I had another Ford that had a bad lifter and I drove the heck out of it.
So, yeah, it's possible, but very much according to what the trouble is.
If that was a case of an o2 sesnsor, you likely spent way more on extra gasoline than you saved in not fixing it.
Actually the O2 sensor has a lot more to do with emissions and the air pump function than fuel mileage. Where it's a complicated system, for sure, most often your mass air flow and throttle position sensor/switch has the biggest effect on how much fuel is being applied.
That's wrong. They aren't independent. It's a closed loop system under most conditions. If the O2 sensor isn't providing feedback, the computer has to make guesses based on the rest of the sensors, but the O2 sensor provides actual, real-time results of how close the fuel mixture actually is. If the system is not sure, it will run on the rich side to better avoid potential damage from an overly lean condition. Potential valve damage, detonation, etc,
The fuel economy can vary significantly - as much as 25%, and that particular number is from personal experience.
On a Mass Air system car I owned (vs Speed Density, which by nature runs by somewhat different logic but still needs the O2 sensor) check engine light went on, car still seemed to be behaving exactly as it always did, but I wound up getting 19 MPG per tank vs my usual 24.
That $18 I spent for a replacement unit was more than worth it.
Nobody can truly answer your question without know what you mean by "engine trouble". Leave the car sit until you can get it fixed if you're not familiar with engines. My truck recently had a misfiring cylinder, runs rough, sucks gas, poor acceleration. Yes I could possibly keep driving it for months, but I did the smart thing and left it in the driveway until I got a new ignition coil. Many engine problems can be fixed with relatively inexpensive repairs so why risk ruining your engine?