At quick glance, I don't see anything really wrong with Adam's math. I guess he should use Ankiel's OBP against righties if he's making the platoon assumption but given the small percentage difference between that stat (about .315) and what Adam used (.298) and the small difference in at bats we're looking at (about what, a little more than 5%?) I don't think you'll see a difference of more than a couple outs, if that.
To be completely picky the question was:
How many outs will the Nationals save by Ankiel hitting sixth instead of second?
Assuming that they just moved Werth-Zimmerman-LaRoche-Morse up one spot each then you'd have to figure each ones increase in outs made (with more at bats) and then figure in that 25 saved by moving Ankiel. Off the top of my head I'd guess it'll probably be real minor change , maybe a couple outs for each one. So you're still probably looking at 15-20 outs saved by the move.
(I could also argue a better lineup means more plate appearances across the board - so that should be scaled up, but really what? 5 more at bats? 10? It's not going to matter)