Social distancing is/can be affective, however it will only be practiced by those who see the severity of the pandemic and what this virus is capable of. Way too many people downplay the severity of what is going on, and follow their own "expert" advice and ignore the warnings from those that actually know what they're talking about. Those are the people that will continue to spread the virus because they're not willing to make necessary life changes if they see it as nothing more than a common cold or a flu.
If everyone was doing it I don't' feel that sates would be going to the extreme of making shelter in place declarations. Unfortunately not everyone takes this seriously and don't necessarily feel that its concerning enough to change how they conduct their day to day life. I simply don't think that social distancing alone is going to slow this down.