Apple TV to Projector via HDMI-VGA adapter works - optical audio-RCA converter to projector does not
We had the same issue in our school environment, with teachers wanting to hook Apple TV devices to their projectors. Instead of buying new projectors, we used the Kanex ATVPRO, which allowed for both audio and video. This allows them to AirPlay from iOS or the MacBooks. We can also stream content from Netflix this way.

As for your specific configuration, I tried several combinations of digital optical to analog RCA, and never got what I wanted. Only the Kanex has worked for me.