This setup should be ok: GoDaddy should let you create the various DNS records you need (MX, CNAMEs for Google Apps, etc.).
One thing you'll want to verify is that Go Grid/Microsoft Azure will allow you to host your DNS elsewhere (GoDaddy) and give you static IPs for your hosted application(s) so that you can create reliable DNS records that aren't going to change.
If that's not an option, you may have to host your DNS records with Go Grid/Microsoft Azure, but you'll then need to make sure they allow you to create your own A, MX, CNAME records for Google Apps (and verify that you can create records for domains that you don't control; I've had "Advanced DNS" packages from hosting companies before that only permitted you to create records for yourdomain.com, so Google Apps was not going to work).