I never got a response that my message was received. Can I just assume they got it?
Mark says he set something up to automatically send a message to the Y!Group's -owner address as soon as he receives the Invite. Bottom item here:
So have a look in your spam folder or anywhere else an -owner message may have been delivered.
That response should happen immediately, whereas the transfer won't actually accept the invitation, and you will not get the "new member" notice, until your turn in the queue.