Can I host Boonex's Dolphin software on Godaddy?

No, no, NOOOOOOO! You can try, and I promise that you will end up pulling your hair out!

Godaddy is fine for plain html sites, but Dolphin needs freedom to swim free! If you want a host that works flawlessly with Dolphin then use Hostmonster! Save Godaddy for the Non-dolphin sites.