Thanks everyone for the replies. To answer a few questions:
I've had the lens for 10 months right now (so I'm trying to send it in under warranty, if possible). I don't recall it always making this sound, however. As I said, there's a slightly louder variant of this sound, too, which worries me more. It's definitely louder than my 24-105 f/4L.
And it doesn't seem connected to the amount of light - I've had it make that sound in many situations (as I can recall).
As for the relative volume of the clip, you can hear the plasticy click of my pressing and releasing the shutter button, and in the first sequence, the AF motor runs.
Thanks all for your responses!