No, you can't.  Khan only posts into Google Classroom.  It doesn't set it up as an assignment on either platform. It's basically a link to the Khan Academy practice in Google. I make my assignments...

1. Közösség
2. Classroom Tips and Tricks
3. Export Scores to Google Class

I just experimented with KA and GC.  I can add an assignment from KA to my GC, but the grades are not recorded.  Since I have the assignment in my KA account, I did get the grade through KA. Anothe...

1. Közösség
2. Classroom Tips and Tricks
3. Export Scores to Google Class