The Dawn spacecraft is in orbit around Vesta as I type. Of the two bodies Dawn will explore, Vesta is the more boring in terms of possibilities for organic chemistry, since it's drier. For Ceres, McCord and Sotin estimate a water contentof 17-27% by mass. This means Ceres actually has more water than Earth's oceans. Of course much of this will be present in minerals and not sloshing around loose, but that's still a much bigger reaction vessel than Urey and Miller had. In fact, if we think water-mineral interface is what matters, which is what underlies the assumption that Earth's first RNA replicators appeared in shallow warm pools where they had surfaces onto which they could be immobilized for more reactions, then most of the volume of early Earth's deep seas could have been an organic chemistry desert, by comparion to Ceres.
Unfortunately we won't know, because Dawn only has EM detectors. My wish for a landing or at least a gas chromatograph on board Dawn stems from my argument that it's exactly on small wet bodies like Ceres that we should expect to find evidence of von Neumann probes, or their descendants.
Above: gas chromatogram of amino acids found in the Murchison meteorite. The organic chemistry of small bodies, even including nucleic acid bases as in the Murchison meteorite">this paper, is usually discussed in the context of being a possible source of early replicator chemistry on Earth; this is not mutually exclusive with these materials being von Neumann probes, mutant or otherwise. Figure from Engel MH and Macko SA, Nature 389, 265-268(18 September 1997).
Both Vesta and Ceres are big enough that you can't reach escape velocity just by running (Vesta's escape velocity is a little less than a jet's at cruising altitude, and for Ceres it's a little more than Mach 1); so they still aren't trivial gravity wells (a criterion for being a good place for replicator activity). However, it looks like water vapor has already been observed escaping Ceres, a necessary step in the spread of an organic-molecule model of von Neumann probes. But I hope that Vesta surprises us, because we have to wait until February 2015 for Dawn's efficient but not-flashy ion thrusters to get it there.
What would be really ironic is if we didn't find anything until we towed a smaller asteroid back to Earth orbit for mining.