In order to understand if birth control pills can facilitate insomnia and lead to sleep deprivation or we look at the birth control pills’ side effects. The most common of them are:

Throwing up or having the feeling constantly
Increased sensitivity of the eyes and/or breasts
Bloating
Headaches
Mood swings (in some leading to depression)

Actually you immediately see that the 1st, 3rd and 4th would clearly create a feeling of discomfort, which leads to increased anxiety, which leads you far away from the relaxed state you need to sleep. http://sleepdisorders.dolyan.com/do-birth-control-pills-cause-sleep-deprivation-or-insomnia/

That was very informative. I do agree that it may have a negative effect. And I guess the entire premise is conducive to such mental states.