Yes. Instead of passing the instance variables from the controller to the view, you instead send it to the client as JSON and basically replace the state of the relevant component(s) (through the ajax callback, or whatever method you prefer).
As your app grows, it might become inefficient to send down the now-huge JSON object, and you might want to add some client-side logic to deal with that. However, this might not even be necessary, as 1) even though you replace the entire state, React will only update what changed, and 2) by using optimistic updating on the client (or whatever the proper term is), the user might not notice that the actual data-syncing is a bit slower. Plus, it'll still be faster than a server-side-only approach.
The nice thing is that sending the total state (of the page or component) every time significantly simplifies matters, to the point where you might be able to keep relying on your server-side framework for most of the logic, at least until you need to start optimizing stuff.
As your app grows, it might become inefficient to send down the now-huge JSON object, and you might want to add some client-side logic to deal with that. However, this might not even be necessary, as 1) even though you replace the entire state, React will only update what changed, and 2) by using optimistic updating on the client (or whatever the proper term is), the user might not notice that the actual data-syncing is a bit slower. Plus, it'll still be faster than a server-side-only approach.
The nice thing is that sending the total state (of the page or component) every time significantly simplifies matters, to the point where you might be able to keep relying on your server-side framework for most of the logic, at least until you need to start optimizing stuff.