Here is a video from a guy who calls himself the Drywall Doctor. He rarely fills corner gaps unless they are a bit large, but he always fills seams with Durabond. He explains why in this video. Check out his other videos as well:
If I were doing this, I would fill in the wider gaps in your corners with Durabond as well as the seams before taping. I would use Straight Flex for the corners, makes taping corners easy peasy!
siffleur