Absolutely NOT! For many reasons:
1) Prime example - the KID, where ...f5 is often played, and the KIA, where h4 is often played, are nothing alike except the first 5 or 6 moves.
2) Many openings are a matter of commitment. 1.d4 f5, the Dutch, is perfectly sound because White's play of d4, making d3 no longer possible, weakens his control of the e4 square, and so Black grabs hold of it. The "reverse", Bird's Opening, is significantly weaker in that Black has not committed to ...d5. Also, even if Black does play ...d5, how Black follows up in the Dutch (if played correctly, many incorrectly play the same moves no matter what white does, which is wrong) depends heavily on what White does. In Bird's Opening after 1.f4 d5, White has to commit first to a plan.
3) Many systems that work for White don't work for Black. In the Reverse King's Indian, Black can play the reverse Fianchetto or the reverse Saemisch, but the reverse Classical is basically busted. The extra move for White is too much while the extra move for White is basically useless in the reverse Fianchetto or reverse Saemisch. The same can be said about the Reverse Dragon. The Classical Dragon Reversed Black has complete equality with correct play. Black does not have time to execute the Yugoslav Attack. He will get crushed with correct play by White.
So NO! Reverse Openings are NOT legitimate shortcuts to studying less. They are their own opening, and should only be used under certain circumstances. For example, the King's Indian Attack only gives White a legit shot at an advantage when played against the French (1.e4 e6 2.d3 d5 3.Nd2 Nf6 4.g3 c5 5.Bg2 Nc6 6.Nf3 Be7 7.O-O O-O 8.Re1 b5 etc.
If you know the theory of one opening (for example, the sicilian:1.e4 c5) would you automatically know the theory for the reverse (ex. reverse sicilian:1.c4 e5)?