Nope - clip ins will not set off the metal detectors in the airport.
Metal detectors in the airport do not detect ALL metals -hence why I can walk through that mess with a headful of bobby pins no problem. And why women can go through with various pieces of jewelry on no problem. It depends on the composition of the metal.
That being said, I assume that clip in hair pieces are made of the same stuff as bobby pins, so it shouldn't be a problem. And worst comes to worse, walk through the metal detector, let the sucker beep, and you stand there shrug your shoulders, they'll wand you and you can just say you have bobby pins in your hair. They won't make you take them out.