It's possible. You just need the right AVR with preouts (at least for the L/R in your case) as well as powered speaker terminals.
It looks like you're not planning to run a center channel and relying on a speaker built into the projector? If so, I'd advise against it, as the center channel speaker is probably the most important in a surround setup, and I'd imagine that there are compromises when fitting one into a projector. There should be numerous affordable options that could outperform the UST speaker.
Additionally, if the audio to the projector is relying on HDMI as opposed to a preout, it may not work, as the AVR may only want to send audio to the sink (the projector) or internally, not both.
The least expensive option to buy new that has L/R preouts is probably the Costco-only Yamaha TSR-700 (clone of RX-V6A).
It looks like you're not planning to run a center channel and relying on a speaker built into the projector? If so, I'd advise against it, as the center channel speaker is probably the most important in a surround setup, and I'd imagine that there are compromises when fitting one into a projector. There should be numerous affordable options that could outperform the UST speaker.
Additionally, if the audio to the projector is relying on HDMI as opposed to a preout, it may not work, as the AVR may only want to send audio to the sink (the projector) or internally, not both.
The least expensive option to buy new that has L/R preouts is probably the Costco-only Yamaha TSR-700 (clone of RX-V6A).