On the other hand, it's also quite possible that the phenomenon of incorrupt corpses occurs regardless of the virtues of the individuals in question, but then corpses of the particularly virtuous are held up as examples of divine grace, while the incorrupt corpses of ordinary people, not being seen as evidence of anything in particular, are ignored.

That is also a possibility. And it can be tested for; if it is true, then the percentage of incorrupt corpses should be constant whether the people were virtuous before dying or whether they were legally executed for crimes committed (and not later exonerated by, say, DNA evidence).

...I have no idea what the results of actually checking that would be, but it would certainly be interesting.

You mentioned before the possibility of militant atheists cherrypicking evidence to support their position. This is certainly a consideration that has to be accounted for, but so is the possibility that the evidence favoring religion only appears compelling because it is cherrypicked. This also occurs to a considerable extent with nigh-certainty.

That is a very strong possibility that must be borne in mind, yes.

Consider, for example, the healing miracles of Lourdes, which Nornagest mentioned above, which have made it an international pilgrimage destination, despite the fact that statistical analyses of the recovery rates of pilgrims do not suggest that the location has any particular healing power. Counting every unexplained recovery, while not counting the nonrecoveries, can create the appearance of persistent miracles.

From the Wikipedia article on Lourdes:

An estimated 200 million people have visited the shrine since 1860,[4] and the Roman Catholic Church has officially recognised 69 healings considered miraculous. Cures are examined using Church criteria for authenticity and authentic miracle healing with no physical or psychological basis other than the healing power of the water.[5]

Both references were retrieved on 5 May 2009, though the second was dated 21 October 2003. There we have a rate; 69 miraculous cures, out of 200 million people (and any number of non-miraculous cures as well, of course).

If there is nothing to Lourdes, then this should be similar to the number of miraculous cures among a random sampling of 200 million people with various illnesses.

(Sixty-nine out of two hundred million is low enough to give the appearance of statistical noise; that's odds of close to one in three milllion)