Asymptomatic carriers are the people who never get sick.
Presymptomatic carriers will eventually develop symptoms, they just aren't sick yet.
The recent news that asymptomatic carriers don't seem to be spreading the virus is regarding asymptomatic carriers only. The people who never get sick. Whereas presymptomatic carriers absolutely are spreading it during the up to two weeks in which they are infected but don't feel sick yet.
Remember, the initial West Coast outbreak was genetically traced back to one guy and the four days between when he arrived home in Seattle and when he got sick and went to the doctor and then into quarantine. In those few days before he was sick, he spread it to enough people that his strain of the virus has been linked to thousands of subsequent infections.
So no, "sick people stay home" is not sufficient to curb the spread.