Is absence of cough in primary complex possible?

In the primary complex, cough may or may not be present. When present it is usually mild.

The primary complex is the initial infection with Mycobacterium tuberculosis. It typically occurs in the lungs, but can also occur in other organs. The primary complex usually causes no symptoms, or only mild symptoms such as fatigue, weight loss, and fever. Cough, if present, is usually mild and occurs in about 50% of cases.