Early in his military career Sgt Avery Johnson was involved in the ORION project (also known as the SPARTAN I project), which we know is the initial attempt at creating scientifically enhanced "supersoldiers"; and as a result of this he, and many of the other members of the ORION project, had side effects. Dr. Halsey, after examining Johnson when the battle of Installation 04 was fought, concluded that Johnson had a very rare disease called Borens Syndrome, this was the ficticious disease that ONI created to cover the identities of the SPARTAN I's. This allowed him to 'shrug-off' the effects of a flood infection.
So to anwer your question, Yes, technically speaking Johnson is infected, but he is more of what you would call a 'carrier', meaning that the infection is in his system, but it doesn't effect him like it does everyone else.
Hope that helps :)