Ok, I know this question was posted some time ago, but I just found it using Google because I asked myself a similar thing.
First of all: No, Gaia won't be able to detect Centauri Bb. But the astrometric method has one strange property: It get's better if the planet is farther away from its host star (as long as the observational time needed doesn't get too long).
So, Centauri Bb is just too near to Centauri B to be detectable with this method.
But I think the real question is: Will be able to find earth-like planets in the habitable zone with Gaia?
The rule of thumb I know is: We need a precision of 1µas to find earth-like planets in earth-like orbits up to a distance of around 10 lightyears. And as GAIA "only" has a precision of ~10µas it just won't be enough.
The Jupiter pulls on the sun with ~15m/s and according to this 2008 paper (http://arxiv.org/pdf/0811.2345v1.pdf) this corresponds to measuring the wobble of a star at 150pc with 20µas accuracy (shouldn't it be precision?). But we don't want to find a 318 earth-mass planet at 5.2 AU distance from it's star. Plugging in 7µas precision, a distance of the assumed planet from its star of 1 AU, a mass of the host star of 0.9 solar masses and the distance to Alpha Centauri of 1.34pc we get a minimum of ~5 Earth masses for the planet to be detectable. This may be off by a factor of 2 or something, but the general result is clear I think:
-The rule of thumb I remembered seems to be correct
-Gaia is not good enough to find earth-like planets around even the nearest stars, but it may find some Super-Earths
I still think astrometry will be one of the best planet detection methods in the future, but we may have to wait for purpose-built spacecraft to really find earth-like planets. Finding planets is merely a side effect of the Gaia mission.
I'm hoping that NEAT (http://neat.obs.ujf-grenoble.fr/NEAT-proposal-summary.pdf) gets funded.
edit: I assumed face-on star-planet systems, so matters will be even worse in the real world.