The reason I doubt that is because I can't smell ants "all the time". And I can definitely smell them when they're disturbed. But most people who talk about smelling ants describe the smell as "damp" or "mouldy" or "earthy", and I have never smelled an ant that smells like that.

The only smell I've ever smelled from them is acrid and acidic, and that only happens when they're disturbed or dead.