Can a mouse live after being dropped off the Empire State Building?

No. A fall from two floors up or more would likely break the cat's legs, and a fall from four floors up or more would almost certainly kill it, unless it got lucky and landed in some bushes.

Cats may always land on their feet, but, like they say, it's not the fall that kills you, it's the sudden stop at the end. Cats are not immune to gravity. When you fall from a significant height, you hit the ground at such a high speed that the impact is nearly always fatal.