Real data collection with N = 2

Sure, but the width of your confidence interval is going to be huge. The more values you have in your data set the more confidence you'll have in predicting the true mean of your data. N=4 isn't very large either. You usually want to see n=20 or more before your CI is going to have much value.

What was your hypothesis? If you conduct a very well controlled experiment you might be able to use two data points to refute a hypothesis, but it depends on what you are doing.

The only thing I can clearly see where the two points would be valid, would be a "trend Line" that would continue data into a realm of low field confidence already.

In other words,it could be used with an analytical machine, say a geiger counter that would clearly and accurately trnslate counts into disintegrations per second. AT the lowest end of the counters quantitative limit we could extend its use by a trend line with two (or more) data points that extend the quantitative limit further down .
Single or double point quantitation points are often used to extend lab instruments useful fields into really low concentration levels.