Is anamorphic for NTSC just a flag to the DVD player and/or TV?
Yes, and for FCP, and Motion, etc. It just tells whatever is displaying that footage to stretch the 720x480 (for NTSC DV) to a 16:9 aspect ratio.
How does FCP deal with anamorphic? If it's just a flag, then can I simply turn on anamorphic and FCP will just "crop" off things assuming it's really a 16:9 letter box clip?
FCP deals with anamorphic as follows: if the anamorphic flag isn't checked, it displays the footage in a 4:3 format. If the anamorphic flag is checked, it displays it in a 16:9 format. Checking the flag does no "cropping", it just stretches it horizontally to a 16:9 aspect ratio.
I think you're confusing letterboxing, which is a non-anamorphic 4:3 picture with black bars at the top and bottom, making the picture within the black bars 16:9, with anamorphic, which is a 16:9 picture squeezed into a 4:3 frame, which if viewed on a 4:3 set that doesn't display it correctly, will appear as if the people are all tall and thin, with gaunt faces.
Anamorphic and letterbox are 2 completely different things. Anamorphic footage uses all available vertical pixels (480 in NTSC DV) to save the image, where letterbox footage uses some of those vertical pixels to save the image, but some on the top and bottom to save black so that when it's displayed on a 4:3 screen it looks fine.
Edit: the best way to see this in action is for you to play around with several things in Final Cut:
Create a non-anamorphic sequence and an anamorphic sequence.
Import some footage that is non-anamorphic, and some footage that is anamorphic (ensuring that the flags are set correctly).
Now play around with putting the footage in the different sequences and see what Final Cut does with it. Notice how the anamorphic sequence doesn't have black bars at the top and bottom in the canvas. Note what the picture looks like, whether it's distorted or not, has black bars put on the sides or top and bottom, etc, as you play around with it.