Should work fine with optical. In the settings on PS3 you can have all audio going through optical regardless of if you're using HDMI or Component (or some kind of converter). It would have to be the same on PS4 otherwise optical would be kinda pointless. The problem though is you might need a converter with HDCP. All content on next gen systems is HDCP encrypted.
Alternatively, you can get a converter that includes audio.
EDIT: Doesn't work with HDCP so you'd have to find one that supports HDCP I think.
Honestly though I'd just save for a new TV. You can get a pretty nice 1080p TV for about $300 now. Another option is to get an HDCP-compatible computer monitor (you may already have one) and use external speakers with optical. My monitor is a few years old and has HDCP so I am able to connect my PS3 to it using an HDMI to DVI cable.
Something like this:
Supports HDCP and it's 1080p. You'd just need audio though optical.