Well the answer is no - at least not yet.
The reason I ask is that United Airlines thought they had. At least someone at United did. And that someone said so on their voluminous website. This is what they said:
Star
United is a founding member of Star AllianceTM, the airline network that offers more than 18,000 daily flights to approximately 975 destinations in over 162 countries. To find out more about the first global airline alliance and its worldwide reach, visit Star
"In addition, Air
Uh?
Our data analyst Antonio Panariello came across this note while researching the alliances for the Airline Business annual examination of the state of the various tie-ups and partnerships between carriers.
As far as we recalled, Aer Lingus had been in an alliance. But that was oneworld, and it had since left saying alliances were not too relevant for it these days.
As for Hawaiian, we had not seen any indication of their alliance intentions.
Air India though is spot on - it will join Star pretty soon.
So, what's the story? United say it was an error and it has since corrected the reference, which now reads Air India and Continental. Star confirms this.
Aer Lingus was puzzled when we asked them - no alliance plans there it seems.
So is this all the cranky typing of a busy web operative, or, as the conspiracy theorists among you might prefer, the accidental revelation of future alliance plans?
Hawaiian seems a potential Star member. It recently signed a new codeshare deal with United.
At first sight Aer Lingus looks a longer shot. But consider this far-fetched link: Star's Lufthansa buys 20% stake in JetBlue; JetBlue forges transatlantic pact with Aer Lingus.
So, an accident or something more?

How about adding this to the mix of speculation?
Lufthansa buys Singapore Airlines stake in Virgin, then pushes them to merge with favourable bmi.
Hence Virgin comes into the Star Alliance fold pretty fast and stops any arguments about the AA/BA tie up, as they too will have to forge anti trust immunity with CO and UA.
All in the making :-)
Interesting scenario Skymaster.
You are right to speculate on what might and might not happen around the future ownership of both bmi and Virgin.
I personally don't think there will be any fast ownership change at bmi - although it does seem likely that it will move to Lufthansa which has an option on the business at some point.
Whether or not the fuel price falls back further, as it has been in recent weeks, I think the chances of deals unless for distressed carriers has diminished for this year.
Everyone wants to keep their treasure chest, however puny, dry for as long as possible simply as a matter of survival.
Aer Lingus were a oneworld member but announced they were leaving at the end of 2006, didn't they?!
I always thought they were a member of Star Alliance though - but have no idea why. Perhaps it's because of United? I'm now rather confused. It's as if something's been erased from history. Weird.