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We rotated a number of good solid players through #2 and #4 spots at various times in the year and they kept NOT hitting with men on base, no matter who they were.  Griffey, Lopez, Beltre, Gutierrez, Branyan...all spent time in BOTH #2 and #4 batting order spots except Beltre and Griffey never hitting 2nd.  Sweeney also hit 4th a lot and he had a good year...just not with people on base.
Incidentally...baseball-reference.com, guys.  Learn it.  Use it.  If you're looking for a split...chances are it's there.
Here's the totals by batting order position:
.837
.673
.735
.731
.837
.710
.578
.689
.617
Not only did Branyan crush the ball in April and most of May hitting 5th...but when Gutierrez got hot, they stuck him in the 5 hole.  Otherwise, there's nothing at all inorganic about the progression of OPS values from 1 to 9.  So no...batting order does not account for the lack of runs vs. OPS.  Not really.