Yes! Your video is automatically saved to your Google Drive account, and you are able to share a link directly to the Google Drive file. The Watch Page does not change that - it simply redirects the viewer to a different page for viewing and gives you the additional benefit of being able to aggregate information on how your video is being viewed.
You can also still share your video through the Google Drive link, although sharing the Drive link for users to watch your video will not allow you to capture analytics.