Will drastic shutdowns like they're doing in italy really be able to stop the coronavirus from spreading?

Depends: The steps taken to reduce transmission work, human nature is what works against it, we all have to comply with mandates, because even a small group of people that ignore the precautions can start a whole new rise in cases

Can be effective: New York City has bent it's COVID 19 curve through strict rules - but not all cities or states have been willing to be this strict.