I assume a modern webpage has some logic to it which besides the redering also needs to be processed and if you apply that to a scale of billions x years I guess yes. But as I said I'm not an expert in the field nor have I any numbers. It's just what I thought.
Edit:
Thinking of having only to serve a state once and having each action processed on the client side instead of making for each a call the backend which has to return a fully rendered page.
The server doesn't [have to] return the entire page on a change. Return small chunk of HTML or small chunk of JSON. There will be a small cost to do the HTML on the server but there is also a cost to do the HTML on the client: sending them 50000000000kb of JavaScript initially.