What happens to an icloud.com address when you delete the Apple ID? If I delete an Apple ID account that is registered with an address@icloud.com, what will happen to the icloud.com email address and its availability?

Specifically, I am interested in deleting that account, but may wish to re-register it and claim the same email handle.

Will the email handle be immediately put back in to the available pool, will there be a delay, will it never be allowed for re-registration... ?
If I delete an Apple ID account that is registered with an address@icloud.com, what will happen to the icloud.com email address and its availability?

According to the support article How to delete your Apple ID account, the icloud.com email address is deleted, that is, messages associated to that address are deleted and you can't use the address to send or receive email:


  What happens to my iCloud mail and messages when my Apple ID is
  deleted? 
  
  When your Apple ID is deleted, all of your iCloud email and
  messages are permanently deleted as well. Any messages sent to you via
  iCloud (Mail and iMessage) are not delivered.


About availability, a couple of years ago I asked Apple to delete one of my Apple IDs and support told me (at that time, you could only make such a request on the phone) that the email address associated with my Apple ID could not be reused as an Apple ID. So I'd conclude that the email address can't be reused.

Specifically, I am interested in deleting that account, but may wish to re-register it and claim the same email handle.

In this case, Apple recommends that you deactivate your account instead:


  If you aren’t planning to use your account for now but may consider
  returning to it in the future, we recommend temporarily deactivating
  your account (where available) instead of deleting it.


If you still decide to delete your Apple ID, make sure that you sign out of all your devices to avoid issues with apps that use your Apple ID account or iCloud. After your account is deleted, you can't sign out of iCloud or turn off Find My iPhone Activation Lock on your devices. If you forget to sign out, you might not be able to use your device when your account is deleted.

Will the email handle be immediately put back in to the available pool, will there be a delay, will it never be allowed for re-registration... ?

As commented above, Apple support told me the email address couldn't be used  as an Apple ID again, so re-registration doesn't seem to be possible.

You may want to contact Apple support to confirm this.