Not in the C4D-internal functionality. And actually it’s fairly difficult to devise a system that can re-establish symmetries after the original symmetry has been broken - how should the system know what other (symmetrical) point to move when the other point had been unilaterally moved away from the symmetric position? Or worse, if the topology has been modified on one side by cutting, inserting points, or removing polys? While there are topology-comparing methods, this is not a trivial task.
Neither is the idea of just applying tools symmetrically on both sides. Internally, C4D has a messaging system that allows to capture point-move, point-insert, or edge-cut events (etc) and duplicate these actions on the symmetrical side. I believe there used to be a plugin that used this system to symmetrize models while working on them, but AFAIK it was commercial.
Some time back I thought about a plugin that simply stores the relationship between two symmetric sides, and is able to transfer point movements on click from one side to the other. This is not that difficult, and maybe I’ll program it in the future, but it will not be able to transfer topological changes like removing or adding points, so it is not exactly what you are looking for.