I have read many times that these lenses are a bit soft for DSO, even though they are good for wildlife and sports. But that should not stop you from trying! Lens performance is subjective, after all.
I could only find a couple examples on Astrobin, but that's the Contemporary version (which I think differs from the Sports version): https://www.astrobin.com/gear/61400/sigma-150-600-mm-contemporary/
There is also the Tamron, not the same brand of course, but that will give you an idea of what can be achieved with similar specs: https://www.astrobin.com/gear/36000/tamron-tamron-150-600mm-f5-63-di-vc-usd/
Also, when I want to find examples pictures with a given lens or scope, I usually type e.g. "astrobin canon 400mm" in my search engine. Astrobin is good for referencing the gear used, and there are always a lot of sample pictures to analyse!