In Google Sites, it is possible to embed a Google Apps Script which has been published as a Web App. You just click "embed" and paste the URL of the Web App. It is possible to use the mouse to resize the iframe. However, I could not set the iframe to be of full width. Is that possible? Also, is it possible to make the whole page scrollable (instead of the iframe) when the Web App has some larger height as well? (I actually don't want to use any other functionalities of Google Sites except that it "hosts" my Google Apps Script with a custom URL and that it gets rid of the standard header warning that this Web App is not by Google).
Unfortunately, AFAIK, this is not possible within Google sites.
I have experimented with various custom iframe HTML and CSS to try and find a workaround, but due to the way the site is rendered, it will always wrap your custom code in its own HTML and CSS. Any solution along these lines seems like it will be unreliable.
If you would like to see this specific functionality you can always submit a feature request.
It let me resize it vertically as far down as I wanted, it seems like full width since it is the only element on the page, and it doesn't present me with the warning.