It wouldn't have made a difference because it would need to recurse all of the way back to Akamai anyway e.g your resolution would look something like this:
* Query the root name servers for the .com zone
* Query the .com nameserver for example.com
* Get back a CNAME pointing to Akamai
* Query Akamai for the address of that CNAME
* Some random error occurs here because their DNS is down
You were either lucky or had the affected domains cached just long enough that you didn't notice.