Yes, hence I mentioned flaking rust. Surface rust, if properly treated can indeed protect deeper layers, more in other metals than in steel but it is a well known concept, a protective 'skin' that prevents further oxidization. Flaking rust is when the rust splits of layers of steel, typically seen in steel that has been 'folded' while being forged. That's not a good thing, it allows water and air access to those deeper layers by creating space where the rust has pushed away the surface layer from the deeper layer.

Even so, those elements the Eiffel tower is made out of are about 1" thick (25 mm) at the base of the tower and there is plenty of redundancy in the design so it's not like it will fall over next Tuesday.

I wonder how you'd tackle repairing it, those are for the most part forged rivets hot joining the steel elements, you could drill them out to replace an element but that would have to be done extremely carefully to first take the load of that element with temporary bracing.

I'm pretty sure the city of Paris will do a lot to keep their iconic landmark, but this will be an expensive operation.