No. Mars having less atmosphere is exactly the point. Such an entry system hitting Earth's atmosphere would be like slamming into a brick wall--it wouldn't survive. And the greater density air on Earth would make the sky crane segment completely unstable. Not to mention that Earth's gravity is simply too large--components of the system would be crushed under their own weight.
I don't know about most of your points, but the components being crushed under their own weight doesn't seem right. The probe was built in Earth gravity and had to undergo 4-5G of acceleration during launch. Also, it's going to experience 13G of deceleration when entering the Martian atmosphere.
Believe it, because it's true.