You could probably guess it by taking a diff of server side requests between a browser initiated dest (header.png) and js initiated dest (/api/user). Yes there would be gotchas around crawlers, adblockers etc but could do for a decent first go.

Also wouldn't be generalisable to the wider internet because 'does the site even work without js' would be a huge cofounder.

Still wish I had access to traffic stats on a large enough site to play around with this.