Are Armageddon chess games fair?

Has any research been done to show that Armageddon games are a fair way to break a tie? If it is fair, then it should end up 50% for both white and black.

If you're not familiar with Armageddon tie-breaker games: http://chess.about.com/od/chessvariants/a/Armageddon-Tiebreakers.htm

After thinking on this more, it seems that because of the time bidding that happens in an Armageddon game, it should be theoretically a fair method. Early adopters will overestimate or underestimate their time bids, but eventually if they see that black "wins" 65% of the time they will adjust their time bid to try and get black.

Or you could just have co-champions this year....

Frankly, I'd rather that than an Armageddon game at the end of an excellent tournament.

I think the US Championship system is 45 minutes vs lowest bid, with the lowest bid choosing their colour.

One of the alternates mentioned in the about article was giving each player a set amount of time, randomly choose colors, then if there is a draw a new game begins with colors reversed, but only the times left from the first game. 

That sounds like a better system to me than a structure where draw=black win with arbitrary time differences. But I've not given it any thought before now. Any reason it would be worse than Armageddon chess?

What about giving the black player the option to play the white pieces after white's first move? Black can either make a move as normal, or chose to switch sides. Or would every game start 1. Nf3?