Mass of Sun = 1.989E+30 kilograms
Mass of Earth = 5.976E+24 kilograms
Mean distance between Earth and Sun = 149,600,000,000 meters

The ratio of their distances to the center of mass should be related to the ratio of their masses. Therefore I calculate the Sun to be about 449,477 meters from the center of mass (composed of only the Sun & Earth).

If the new SIM instrument has micro-arcsecond resolution, that is the same as being able to distinguish an angle of 2.8E-10 degrees. From the trig relations of a right-angle triangle the farthest distance at which an Earth-like planet could be detected by the "astrometric wobble" of its star would be approximately 9.197548246E+16 meters. That's equivalent to 9.72 lightyears.

Proxima Centauri ---> 4.2 ly
Alpha Cen A ---> 4.3 ly
Alpha Cen B ---> 4.3 ly
Barnard's Star ---> 6.0 ly
Wolf 359 CN Leo ---> 7.7 ly
Wolf 359 BD +36 2147 ---> 8.2 ly
Luyten 726-8A UV Cet A ---> 8.4 ly
Luyten 726-8B UV Cet B ---> 8.4 ly
Sirius A Alpha CMa A ---> 8.6 ly
Sirius B Alpha CMa B ---> 8.6 ly
Ross 154 ---> 9.4 ly

Four of those are binary stars. So there may only be 7 actual systems, and can a binary system harbor a terrestrial planet? It's a fair bet it wouldn't be anything like Earth if it did.

Doing the same calculation for Jupiter yields an "Astrometric wobble" of 743,502,765 meters. From the trig equation d = wobble/tan(alpha) where alpha is the angular resolution from earlier (2.8E-10 degrees) we get a range of 1.52E+20 meters, or 16,081 lightyears.

Clearly they should detect Jupiter-like gas giants half-way to the center of the galaxy! But I don't think they'll find any terrestrial planets without greatly improving resolution.

If we assume that most stars are 5 ly apart then the number of stars within r lightyears is approximately:

N = 0.064*r^3

To search 1000 stars for terrestrial planets requires a search radius of 25 lightyears. To detect a planet exactly like ours orbiting an identical star (same masses and distances) would require an angular sensitivity of 1.088835409E-10 degrees, or 0.391 microarcseconds.

Actually not a bad result. They may have to improve their measuring sensitivity still by less than a factor of ten.