I read the first post and did some testing myself. In order to fully explain what I did, I'll have to tell you what I have:
I started using Apple when is was still .Mac, so I have an active @mac.com address. That was later "upgraded" with an @me.com alias (which I don't give out or use). I also have an info@"myowndomain".nl and a work-email (patrick@"work".nl)
Because I'm still using my MacBook Pro 1,1 (Core Duo), I wanted to test an additional iCloud account for my iPhone 4 without the risk of loosing access to my Address Book etc. And boy, am I glad I created that test-account!!!
So to sum it up so far:
MM@mac, MM@me, info@, work@ and iCloud@me (Are you all still with me??)
I created a new event on iCloud.com and invited my other four mail adresses. Only ONE invite made it to Mail.app, which was work@. Amazingly enough the event did show up in my iCal 5.0 calendar. Twice to be exact (one for MM and one for info@). I did get notifications from the app, but not in my e-mail... :-S
On iCloud.com I turned the "pref" for using iCloud only to recieve events off for my iCloud@ address. First I deleted the first invite. Same thing happend: 1 email notification to work@. But the event did disappear from iCal. Then I made a new invite on iCloud.com. Exactly the same as the first time and not very surprisingly: the exact same results... Also deleted that.
So I logged on to manage my MobileMe AppleID. It turned out that my MM@mac was set as my primairy address. And MM@me and info@ were both registered as additional addresses. So I deleted the last two, leaving only my MM@mac. And work@ was abscent from this list all together, btw.
Then I proceded once again to create a new invite from iCloud.com to my other 4 e-mail addresses. (Just like the other two times). Again I did get an invite in my work@ mailbox, but now also in my info@ account. YEEY. Still nothing on MobileMe, though...
But the event did show up in iCal again: once for info@ and once for MM.
Only one invite and iCal placing for MM makes sence, because @me.com it merely an alias, not a different mailbox ;-)
So.........
My conclusion is now that this is truely a problem on Apple's side, not Google or anyone else!
As soon as an email address is linked to an Apple ID, it will remain in the iCloud. If your Apple ID is still on MobileMe, then everything works just fine. (Yes, I did that reverse test as well.)
Also it seems that the .ics file is correctly pushed from caldav.icloud.com to cal.me.com, while the email sending it gets stuck with its head in the iCloud.
I suspect it will have something to do with that both MobileMe and iCloud are using the @me.com extention. And to be honest, as soon as I heard that new iCloud members would obtain @me.com addresses, I wondered if that wasn't going to lead to some serious trouble... Turns out: YEP.
Apart from that, I do believe that Apple should thurn that "pref" off by default!!
I think there are so many people that created an Apple ID just to have access to the iPhone App Store and linked that to their third party email account, but do not use their @me.com mail address nor ever log on to iCloud.com. And for Apple to make all those people log on just to click off one checkbox??? I don't think so. Do you??
Well, anyway, I hope this helps. Any questions? I'll be happy to do some more testing :-)