FWIW, back when I had the original Motorola Droid, I had to have it replaced 4 times under the Verizon extended warranty (once for a problem with the keyboard, once for a straight-out-of-the-box radio problem with a replacement they sent me, and twice for the headphone jack developing intermittent connection shorts). Each time I sent them back a rooted phone (the first one I actually rooted just before sending it back just so that I could do a nandroid backup to restore to the replacement phone). Verizon NEVER gave me a hassle. They NEVER even mentioned that the phones were rooted. In fact, when I arranged the first replacement I told the Verizon guy on the phone that I would need time to root it in order to back it up since that's the only way to do a complete backup.
That was over 2.5 years ago (I had an HTC Thunderbolt for 2 years that NEVER had a problem, and now I'm on a Galaxy S4), so I don't know if Verizon's policy has changed. But given that it's an extended warranty we're $8 a month for (the TEC package), I suspect they don't really care when it is truly a hardware problem.