The number of PAs that each slot gets is absolutely a part of the equation.
Here's the data on the average number of PAs per game and roughly the number of PAs for the year for each slot in the batting order:
1 4.83, 782
2 4.72, 765
3 4.61, 747
4 4.49, 727
5 4.39, 711
6 4.26, 690
7 4.14, 671
8 4.02, 651
9 3.90, 632
Here is a link to an article containing some of the data, organized neatly into tables, that goes into optimal lineup construction.
http://www.bluebirdbanter.com/2012/10/12/3490578/lineup-optimization-part-1-of-2