On a 4cyc, it doesn't have a down stream O2 sensor, so it won't know or really matter.
On a 6cyc, it has a down stream O2 sensor, the computer will try and try to compinsate and throw codes and run like crap.
Depending on what state you live in, it can be a bit of a fine to get caught without one. In my town, I've seen random smog test checkpoints on the road. Would hate to get busted at one of those.
It really depends what the motor is and what you want to do. In California, you can avoid issues with emissions by registering as off-road use only, but it requires you to never drive it on normal highways.