Will a sleep aid with melatonin, valerian extract, hops - humulus lupulus, passionflower, chamomile have any affect on the birth control pill?

Unknown. That's one of the problems with botanicals, there aren't any controlled studies with which to reference when it comes to drug interactions. I recommend you start with the birth-control and look for drug interactions on the package insert. Even with proper use of oral birth control pills there still is about 1% failure rate.