Since early in their creations, I have been a very, very frequent visitor to the HBD, Eugenics, and New Right Subreddits. Most visitors to Subreddits appear to sort posts by hot or top, not new. I sort by new, often providing the first up or downvotes. Though I have no way of quantifying it, my initial votes appear to affect the numbers of upvotes, downvotes, and brilliant readers many articles eventually receive.
So if you want to have a tiny bit of influence, vote away.
Such a strategy is largely worthless on more popular Subreddits. There's little point in downvoting a cat photo that already has thousands of upvotes. Also, initial votes seem to have less influence now that Reddit instituted a delay in showing vote totals.
Though vote totals are irrelevant to the logical merits of articles, so much media exists now that time starved readers often find the voting systems useful.
Far from being a downvote brigade, I upvote about three or four times as often as I downvote, though I have been a one man curse on Yahoo's and Bruce Charlton's upvote totals.