Well, I know nothing about that Logitech. A common configuration is for the subwoofer unit to provide the power to the speakers via some wiring scheme. So the RCA jacks on the powered sub are likely powered. I am guessing just to make that clear.
The receiver does not have powered RCA jacks. The RCA jacks on the receiver are line level inputs. It has speaker terminals.
Another problem is the subwoofer. The usual system for AV receivers is to send the bass/LFE signal via a line out jack to the sub.
This creates quite a little wiring mess. You can probably hook up the bass/LFE from the receiver to one of the sub's inputs. It should send the low frequencies to the sub, not to it's speaker amps (if I am correct in how it works.)
Then you would have to wire speaker outputs from the receiver into the RCA inputs on the speakers.
You also risk overpowered the speakers seeing how they are probably rated for a 25 watt amp. Maybe not a huge concern, but something to consider.
In short, it's a bit like trying to fit a square peg into a round hole