Can a carrier of mono pass on recurring throat and/or tonsil infections to a co-worker?

Possibly: Ebv spreads through bodily fluids e.g. Saliva and blood. So if you share saliva or bodily fluids with your co-worker, you could infect them and pass those infections. But most people aren't sharing bodily fluids with co-workers. A lot of people have/get ebv aka mono. Most of us will get it before we die. Thus, perhaps your co-worker already had it or got it from someone else).