Turning off the audio

Yes. FCP < Audio/video settings < audio playback choose an output that you currently aren't using such as Firewire DV (if you have a firewire device hooked up) or digital output if you aren't using that.
 
That said, iTunes is a big system resources hog and could occasionally cause a crash or frame loss on less powerful systems especially with low RAM while you're capturing. I'd get an iPod :)

-Noah
 
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