Certainly you could embed a JS derived client timestamp and send it back appended to some other request, but it's completely unreliable since the user could set their client time to anything they want, and it requires that second request which could be slightly abusive, or technically awkward to ensure. A lot of implementations will do this by fire-and-forgetting an AJAX request for a text file, or adding a single blank pixel image to the page.
You could try and derive a similar metric based on first requests and geolocating an IP - location and GMT timestamp giving you a local time - but that might be expensive if you haven't got an IP/Geo database already :)