It would make sense that it wouldn't affect batting average or home runs, since home runs are measured as a raw number and BA doesn't count walks as at bats... It might not make a big difference as a statistical figure, but it does come into play in the 9th inning, the only time any strategy is employed these days, as there's no way to make up an unlucky run. It also turns sluggers who can't run into high OBP players, putting them where they do the least damage. In the 9th, however, they can be replaced by faster guys who do pose a threat on the basepaths. No manager would pinch run a slugger in the 5th inning, many wouldn't unless they were sure it was his last at bat.
The lineup can be a big strategic factor in the 1st and late innings, but the middle innings are largely left alone and little strategy is employed.