Better cables will only matter if the existing ones are damaged or garbage and when I write 'garbage', I mean really crappy cables that just don't work well on an absolute level, not some "I want my cables to make me a whole person" thing.
However, most equalizers were designed to be connected to a Tape loop on a receiver or integrated amp. On an AVR, you would set RecOut to Source and connect the equalizer's Out jacks to a set of Tape Input jacks. Some AVRs don't work well with processors this way and it may require some messing with the setup to get it to work flawlessly. Equalizers really want to see the tape loop, not the signal and impedance from a volume control