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Sure they can. There's really no way of blocking it except for never connecting it to iTunes or taking it out of airplane mode. Does Apple care or will they do anything about it? Extremely unlikely.
 
Like what if you call apple care? Or if your phone sends in diagnostics. What's the best way of preventing apple to find this out?
 
Like what if you call apple care? Or if your phone sends in diagnostics. What's the best way of preventing apple to find this out?
They are only going to care if you are trying to make a warranty claim. If you are making a warranty claim then restore and remove the JB
 
They are not monitoring your phone when you call them. That would be way too much work for the small amount of time they will be talking to you.

They cannot reach through your phone (whichever one you are calling on), examine your iPhone and then smack you upside the head with it for daring to call them while your phone is jailbroken.

If they ask you to send it in for repair/replacement, back it up, restore as new (which wipes the jailbreak) and then send it in.
 
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