Can I peek at the cards under Bomat Courier whenever I search my library?
You can't look at the cards under Bomat Courier. The card's reminder text even says so explicitly. The fact that you could deduce that information doesn't change it.

This is covered by rule 406.3:


  Exiled cards are, by default, kept face up and may be examined by any player at any time. Cards “exiled face down” can’t be examined by any player except when instructions allow it. [...]