Should the cell sorting marker genes be excluded during clustering?
I do not think there is a simple "yes" or "no" answer here. 

A good starting point would be, as you suggest, use all the genes and assess the results in the light of the marker genes and expected results. This could both serve as as good quality control as well as give you overview of all the processes happening in the cells. 

Depending on the marker genes effect and biological question you may then want to remove the marker genes with potential ordering effect, or even other genes, e.g. by GO terms or pathways. 

You most likely want to account for the cell cycle phases as well. And check for other technical factors. I recommend Bioconductor pipeline to get inspired https://www.bioconductor.org/help/workflows/simpleSingleCell/ when it comes to scRNA-seq analyses.