Nope. No matter how hard you press down on the other side with the hydraulics, you are NOT shifting all the weight of the main unit off of the near side. No matter how hard you push, the overall center of gravity isn't changing.
Sit on one side of a dingy. Now put your foot across it to the other side. Sure, just moving your foot over there transfers a bit of weight, but pushing down as hard as you can on that far side with your foot doesn't change the fact that most of your weight is being applied under your butt cheeks.
In fact, as he pushed hard enough to tip the main body of the excavator rearward on it's tracks, he actually moved the center of gravity even more into the oh-crap zone.