Yes, but as long as a cached version is still returned at the edge (while the real content might have changed), the ETag won't help.
It can only save you from unnecessarily downloading content you already have - in case it didn't change.
And when the content is updated you return different etag and the content is refreshed. Your system should have either distributed cache or a way for the edge to detect cache invalidations or for you to manually invalidate the cache on the edge.