I’m not sure what’s more amazing — that this has been broken for five years, or that someone once thought this was a clever idea, or that almost no-one understands what’s wrong…
I suspect few people use iCloud Calendar invitations — or else we'd all know about this. It's not a new behavior, it was first documented in 2011. It's still true.
It's important to know about this.
When you send an event invitation to an email address iCloud will look up the person associated with that email address (possibly using Contacts). If that person has an iCloud email address then the invitation will go to their iCloud calendar. No email will be generated. If they don't actually use that iCloud calendar they will never see the invitation.
If the invited person does not have an iCloud address in contacts then an email will be generated.
So if you invite with a gmail address, and iCloud finds an iCloud address associated with the gmail address Contact (see update for correction), no email will be sent to Google Calendar. Instead an iCloud Calendar event will be created.
There is such a thing as being too clever.
Some details are here: http://apple.stackexchange.com/questions/27449/icloud-calendar-not-sending-invit es/29970
I discovered this while doing research for a book on using smartphones to support independent living for special needs teens and adults. Using my sister’s iCloud calendar I invited myself using my gmail address. I didn’t get an email, and her iCloud account didn’t show a sent message. Google found the 2011 StackExchange comment so I checked my unused iCloud calendar. There was the event, waiting acceptance.
A wonderful example of how being clever can be stupid.
A family member tells me her iCloud invitations appear to recipients with a name that is only associated with the Apple ID she uses for iTunes purposes — because it’s on her credit card.
This suggests the AppleID lookup is based on the email address associated with one’s Apple ID, not on anything in Contacts.app. I visited the AppleID associated with the iCloud calendar that my test invitation appeared on, and it is associated with two non-Apple email addresses. One of them is the gmail address I used in the test invitation.
Note that many people have multiple Apple IDs. I have four. More, Apple now allows one to have an Apple ID with a non-iCloud email address. Note also that it’s been four years since Cook promised Apple would find a way to merge Apple IDs.
This is my new “Apple FUBAR” example.