Yes, the test will be able to detect IgM/IgG in asymptomatic people, as they will have an immune response even though they don’t display symptoms. The timeline of infection will be the same as someone displaying symptoms.
The fact that the test can detect asymptomatic patients is essential as it can help mitigate one of the most anxiety-inducing concepts in the COVID-19 pandemic - the possibility that you may have unknowingly infected a loved one. This can easily happen with young, healthy people who are infected without knowing it, and recover well from the virus, sometimes never showing any symptoms at all.
During this time, these asymptomatic patients may accidentally infect others. Taking an antibody test will help inform you if you had the virus, and therefore can help you inform your loved ones and encourage them to take the appropriate steps.