Anti-inflammatory properties of andrographis supplements that are effective against other respiratory viruses, such as the common cold, mean that it likely helps to relieve similar, mild symptoms of COVID-19 like a light cough.
In fact, injections of the active component of the herb, andrographolide, were used to relieve people of mild COVID-19 symptoms in Thai hospitals during the pandemic.
However, there's not enough research-based evidence to claim it's an effective cure when taken as a supplement.