This would save a bunch of unnecessary allocations, and it is entirely safe since the state can't be modified between Renderer::render being called and the DomNode being drawn to the page. However, I don't think this is possible without ATCs, as the lifetime of the returned DomNode would be dependent upon the lifetime of the reference to the application state.
The modified Renderer trait might look something like this:
pub trait Renderer<State> {
/// Type of the rendered `DomNode`
type Rendered<'a>: DomNode + 'a;
/// Renders a `DomNode` given the current application state
fn render<'a>(&'a self, &'a State) -> Self::Rendered<'a>;
}