The main purpose of the O2 sensor is to keep the right fuel mixture for the catalytic converter to stay hot so it can clean exhaust leaving the engine.
With that being said the engine has to be in a fairly steady state so that the adjustments can be made correctly.
The sensor can operate under mild acceleration but at a certain point, the fuel gets determined by a fuel table.
I'm not positive but from my experience with my Suzuki 1000, it seems that the ECU wants to keep the hair fuel ratio somewhere around 12.0 while under steady engine conditions. The reason I think that, is that I tried to tune my cruising fuel to a leaner setting in order to save gas, but it seemed like the tuning didn't work very well at cruising. However, tuning full throttle was easy and results could be seen on the first attempt.
Lastly, if you read Suzuki repair manual they show a block diagram that gives a very basic hint to how the sensor gives feedback to the computer or fuel tuning. Of course they don't give you great detail so I cannot say what percentage that it has an effect.
I know this is a lot to read but I've spent a lot of time thinking about how to defeat the O2 sensor but also use it to my advantage.