I have dealt with several oxygen sensor equipped systems in the past and all of them, none were Jeeps, operated in a similar manner: The system ran at an "open loop" setting unless it was receiving a signal from the O2 sensor.
For Example: Volswagens are set up to run VERY rich if there is no O2 signal, but they will run. The excuse for this richness is that it will not burn up an engine, like a lean setting will.
A honda that I had would work quite well with no O2 sensor - the engineers set the default open loop pretty close to what was seen in normal operating conditions at sea level.
I would hypothesize that if you set the carburetor to the proper mixture without the O2 sensor hooked up then you would have no issues. The O2 sensor usually serves to lean the mixture for improved emissions and fuel economy. If you get it set right you will just be operating like a normal carb without the leaning benefits of the feedback carb.
Or perhaps I'm talking out of my *** when it comes to Jeeps...