Yes, remanufactured parts are totally within the terms of your warranty.
Most remanufactured units work just fine; I now that for our cars in particular, there's a software bug where Mitsubishi (who makes the audio system) has inexplicably and randomly been having dealers swap out the screen for a unit with the upgrade. (I had that problem myself, but I ended up being part of the random customers where the dealer got sent a USB stick instead, which I was fine with.)
Most remanufactured units work just fine; I now that for our cars in particular, there's a software bug where Mitsubishi (who makes the audio system) has inexplicably and randomly been having dealers swap out the screen for a unit with the upgrade. (I had that problem myself, but I ended up being part of the random customers where the dealer got sent a USB stick instead, which I was fine with.)