Not exactly...
The rebar can continue to rust inside the concrete under certain circumstances which causes it to expand. This causes the concrete crack and pieces to start breaking off which is called spalling.
They make epoxy coated or Hot Dipped Galvanized (HDG) rebar to prevent the corrosion and spalling.
I did an internship in college and worked on a project at NIH where they were using hydro-demolition robots to take off the the top half of a concrete slab to expose the rebar. Then cut out the old rusted rebar and replace it with epoxy coated rebar and re-pour the concrete.
Camera fades into a boardroom, where a meeting is taking place between two sets of people, some in suits and the others in "work clothes"...
Man in suit..." so what you're saying is we have to slice off the top of the already poured and cured concrete slab, cut out the affected rebar which is embedded in that concrete, lay in this newer, more expensive rebar in it's place, glue the whole thing down and re-pour the top of that slab?"
Man in work clothes..."yep."
Men in Suits heads then explode.
Awesome. I'ld pay to see that movie.... we'll call it CAD Men and it's about the hijinks of a group of designers in the first part of the '70's.....