$\textbf{Answer}$

Yes.

$\textbf{Analysis}$

The Empire State Building is about $100$-story high. Therefore, a stack of coins of that height can be broken into about $100$ stacks of coins. Each stack is about one story high (If we consider one story of the Empire Building is higher than one story of a normal room, then we can break the original stack into  two hundreds piles). Now, it is obvious that the target is achievable.

$\textbf{Note}$

This type of brain teasers try to create a scary mis-perception. The best way to solve them is to keep clam and do the analysis.