I'm not sure if you can drive around without the front axle shafts on. From looking at it I would say yes.

Just an update: I replaced all the rotors (2 were defective). They look like they were cast wrong. The vibration has been lessened quite a bit. Now it's onto those driveshafts. I'm going to get 2 used ones and replace the u-joints.

I've examined the front one and found the u-joints to be quite stiff. I'm going to try to get greasable ones for when I put in the new driveshaft.

I also don't expect GM to replace them. I always say that warranties are pretty much useless. It's very very rare that a warranty is actually helpful. You first have to convince the dealership mechanic that something needs replacement, and that's the hard part. Typically when it comes to vibrations you'll find yourself spending thousands on the wrong things. So, better bet is to just spend money on what you know is messed up and replace yourself. It's easy enough.

I also think the ride is quite bad due to the z71 suspension package. I am going to swap the front coils out for softer ones. You can feel EVERY bump in the road with the z71 suspension, it's quite annoying to say the least. It also doesn't help because no road is perfectly smooth, so every single interstate feels like it's rippled. You can jump on the front bumper lip to try and rock the current suspension and literally nothing happens. Even someone I know who weights 250lbs couldn't get the suspension to move. It just squishes the tires.