Yes, that is the way speaker-level subwoofers are designed to work.  However, do not splice your speaker wires into an RCA plug: that could be incorrectly plugged into a line-level input on a sub, which would be very bad (because speaker level is several times the voltage of line level).  Obviously you need a sub with both speaker-level inputs & outputs as well as the more common (in 21st c.) line-level inputs. If you find an old passive subwoofer, it, too, gets spliced into the speaker cables between the amplifier and the speakers.  But such an old subwoofer might lower the combined speaker impedance beyond what the 4500's amp can handle.  Therefore, if buying, purchase a modern powered subwoofer, which usually has a very high impedance on its speaker inputs, making it "invisible" to the amplifier.  Normally, one wouldn't even mention this, but you said you were driving two pair of speakers, thus might be nearing the 4500's amp power limit?  Additional reading:  https://nucoustics.com/blog/connect-subwoofer-to-speaker-level-outputs/ or https://hometheateracademy.com/connect-a-subwoofer-to-speaker-level-outputs/ .

this is super helpful, thank you for the advice and articles.