Best answer by AjTrek1
At this juncture Airplay requires the use of an Apple Airport Express in conjunction with the line-in of a Sonos Play 5, Connect or Connect AMP. Click the link:
That said using Apple TV as you have diagramed should work. In fact the Apple TV remote will control the volume level of the Playbar. The settings are in Apple TV menu.
You might use your iPad to mirror images to your screen via the Apple TV. According to the Epson EH-TW6700 manual that would be the only way for iPad audio to play through the Playbar; otherwise it will only be heard through the Epson’s built-in speakers.