A recount usually means less than one percentage point between candidates or issues. It is this very type of politically charged situation that the human factor must be taken out of the equation for fairness to prevail. There is way too much chance of fraud and cheating when the people who work in the courthouse, for the elected officials, do the counting. The voting machine doesn't take sides, it just calculate results.
No, it is not possible to have a meaningful recount from an electronic voting machine since such machines automatically figure and tally their counts. There is not as much of a margin of error as there is from hand counts, so a recount on such machines is essentially a meaningless formality.