I wouldn't go out of your way to tell them you are rooted, simply because that sort of thing is on a need to know basis, but realistically, I have gone in for hardware only issues while rooted and they don't care. Then again that could just be a cool rep, in fact I know he was cool because he wanted me to root his phone too.
As mentioned before your experience can/will vary. But its been my experience that if your phone is broken because the phone itself is defective and not because YOU had a horrible debacle of a flash they are pretty helpful. Keep in mind that is the store, if you completely bork your phone and try to make an insurance claim THAT is a totally different story.
At some point (it may be weeks or even months after you send your phone back after it is replaced) it will be inspected, most likely by a fairly knowledgeable early to mid 20's college student who fixes phones as a part time job... had a friend that did it for years. When they discover that your phone is anything but stock, they will immediately conclude that you a.) violated your terms of service by unlocking/rooting/installing custom firmware, and b.) any and all problems with your phone are the result of you (the end user) tampering with it when you were specifically told not to. The end result being that your phone is not covered for that claim, and you now get to pay full retail price for your replacement phone (or if its a refurb, the cost of the refurb).
The only way for them to not know that your phone was tampered with is if it is made non-operational, or is completely restored to stock. But chances are if you brick your phone and make an insurance claim they will find out, unless you are really good at CYA.
Samsung Galaxy Nexus || 4.2.2 || AOKP || 'nuff said
Know your role and shut your mouth.