I don't think that you can. You will not have calibrated down to the level where the peak is too small to find (would you ?? it would be strange to run a calibration and then set minimum area above the peak area for the lowest standard)
No, of course not.
so if you do a calculation based on the minimum area setting you are extrapolating from the calibration.
This is true. I very often set a minimum area to prevent the software from intepreting noise as microscopic small peaks (I know you can do this also with minimum width etc, but minimum area is very convenient). I don't feel uncomfortable with extrapolating from the calibration. Very often you don't need to calibrate close to the LOQ. Then why define an LOQ which is absurdly low?
Calculation example: My minimum detectable area is 0.01, my smallest calibration standard has 15, highest standard 300. I tell my chromatography software to ignore everythin smaller than 1.5. Works great. I know every chromatogram where the software does not find a peak is at least 10fold lower in concentration than my concentration range of interest. If I then define the concentration 10fold smaller than the lowest calibration standard, this is not really the limit of what is possible, but safly (IMHO) defines the useable range.
There is also the danger that the software misses the peak because it has moved a bit, it has something else on top or next to it, or the slope parameters were set wrong.
This has nothing to do with minimum area setting. This is another problem I have to deal with quite frequently...