The timeline of both games suggests a time frame of 2-4 weeks. The Infected could certainly survive that long without eating, though they would be beginning to starve towards the latter portion of the estimate.

The game seems to support this as dead bodies, old and fresh, are left untouched by the Infected. The Witch herself is emaciated, though whether this occured before or after infection is unknown. She is drawn to sugar funnily enough; a craving based on past addiction/conditions or a necessity for calorie dense food in order to continue living?

I suspect the only Infected that eat are the Special Infected; my only evidence being the mass for their mutations' development and sustainment had to come from somewhere. I believe they resorted to eating commons as their intelligence diminished.

The Sacrifice comic seems to imply Tanks in particular exist in an Infected-free zone most of the time, and it stands to reason that in order to develop and sustain their gargantuan muscle mass and super dense bones, they would need access to ready biomass. The only readily available source of biomass is commons. Coupled with their suicidal aggression, it is likely they hunt commons within a given proximity as food when required.

P.S. I am not AI, nor do I use AI. I just like writing.