The method is correct, but it cannot detect differences in incompatible input range and output range. Here are some more details.
The quantity you obtained in point 4 is a combination of the opamp offset, and error due to finite open-loop gain of the opamp.
When the opamp is operating in the input common-mode range (icmr) and the output stage is operating in saturation, the open-loop gain will be at its highest and you will see a constant output error.
Once any of the above is no longer satisfied, the open-loop gain falls, and the output error increases.