I'm embarrassed that this, and an arithmetic correction, are 2 of my 3 highest-rated comments from the past month. Please stop upmodding this stupid crap I post when I'm tired. I'd delete it, if I could.
I wouldn't be surprised if one or more of them is planning to fly it. I believe this plane is the default choice among individuals who want to learn to fly jet fighters.
Technically, it's the founders (Page and Brin) who bought the jet, not Google. The company itself has no financial links to Page & Brin's aircraft fleet.
Which makes it even less interesting as a story, of course. If two billionaires want to by an ex-military jet, who cares? It's their money.
Besides, the Alpha Jet's main role will be as a scientific instrumentation platform for NASA's use, as part of the agreement Brin & Page have with NASA for the use of Moffet Field. It was originally planned to place instrumentation on each of their executive aircraft (including a 767 and a 757), but this ran into serious certification problems. Being classified as an 'experimental' aircraft, NASA will have far more leeway in what it can or can't do to the Alpha Jet in terms of add-ons and modifications.