After a 3-week wait, I finally got my MBA back. I'm in the US & I made the purchase in July '12.
It was 2.5 weeks before the part I needed finally came in, plus 24-48 hours for the SSD to be installed. I got my notice by email that it was ready around the 36-hour mark.
Something's up with a certain brand of SSD's because although they ordered a particular brand (not sure if it was Toshiba or Samsung -- I forget which), another brand was sent instead. This caused a further holdup because the part numbers weren't matching up.
Anyway, not the best experience considering I had Apple Care to prevent this sort of delay, but there were a couple of Apple employees that proved helpful, for which I'm grateful.
The key with all of this is persistence. Especially when dealing with the phone reps because their responses are mostly canned and they're not really listening. Plead your case or ask to deal with someone with more authority who can address your issue.
Good luck to everyone!