Can one exclude calibration points using a combination of permutation testing and a non-parametric test statistic?
This is more of a comment, but a typical comment doesn't allow a figure...

You have a very wide range (1-1000) for the independent variable. Using a simple linear least squares analysis isn't appropriate. 

I grabbed the image below from webpage https://www.mathworks.com/matlabcentral/answers/392636-confidence-band-around-linear-least-squares-line



The point I want to make is shown by the shaded area. Assuming homoscedasticity, you wouldn't weight the errors. Thus the confidence interval for the line is narrowest at the center of the fitted range and gets much wider at either end of the range. So your low samples ( 1, 2, 5, and 10) will essentially be irrelevant. 

So you need to assume hetroscedasticity and weight the sample errors somehow.




  1. Does the proposed test statistic seem reasonable as a non-parametric replacement to the t-statistic?


Just because in general non-parametric tests are less powerful than parametric tests, I would try hard to avoid using a non-parametric test on parametric data. 


  2. Is it appropriate to exclude samples from the regression, for which the p-value for the test statistic exceeds the defined threshold?


I'll assume that you mean to exclude some of the standards not samples. It is possible to exclude standards, but don't use three standards and then drop the one that you "know" isn't on the line. :-)



Hope this helps a little. I just don't know enough about S/N for LC/MS or the detector system that you're using to tell you what you should do. 

Your statement "Given that, for many compounds, the data are often non-‘normal’ around the lower-end of the calibration curve in such dataset,..." is disconcerting.