Depends on your codec, FCP settings, and lots of other things. A few basics first: 23.976 fps footage isn't going to playback at that frame rate on a NTSC device. It's going to playback at 29.97 so if you're working with SD or Widescreen NTSC projects you'll have to render your 23.976 comps to 29.97 fps interlaced with pulldown to make the footage work in a NTSC project.
If you're going to DVD you can use the 23.976 (often displayed as 23.98) footage most of the time because most DVD players will see the frame rate and output a 23.976 fps signal through the composite or component video outputs. Older ones won't. The only way to see NTSC sized projects with true progressive frames and undistorted is to send the 24P footage to a flatscreen that will actually run at 24p through a DVD player that will actually playback at 24p.
If your project is for BluRay or HD, then you can safely work exclusively in the 24p frame rates.
You need to make sure that your FCP sequence is set to 24p and that your footage is interpreted as 24p. Also, don't make the mistake of thinking your footage is 30P because of the timecode display in FCP. NTSC Drop Frame time code, which displays accurate hours minutes and seconds but does not drop any frames, is based on 30 (29.97) fps so you can end up with a frame number that does not correspond to the actual frame number of the footage.
I've probably confused you a bunch, but I hope the explanation helps. Most video codecs are automatically interpreted by AE, PPro, and FCP. Most of the time the interpretation is correct, but sometimes you need to make adjustments to make things work correctly.