No, it will not. What is allegedly better in ZXR than on your integrated, is the DAC section. DAC stands for digital to analog converter. If your PCM bit stream (the audio data) is never converted from ones and zeros (digital) to a continuous (pre-)amplified voltage signal (analog) before sending to your receiver (ie: you send it in DIGITAL form), you will completely miss out on the sound quality benefits of the ZXR (less noise floor, less distortion, flatter frequency response and possibly better channel separation), because the receiver will do the DAC conversion for you. The ZXR doesn't do any magic to the data (your files, your games sound samples and sound engine's work) that would make the sound any way better, especially if you use HDMI which is a connector on your GPU and completely bypasses the ZXR.
IF you use the S/PDIF Optical connection from the ZXR to receiver (that is to say, the ZXR is somehow involved in sending the data to the receiver), AND you use the effectifyer crystallizer x-fi virtual surroundifyer ultramega 360 noscope Dolby features in the ZXR settings on your computer, then the digital bit stream will be different, but it will only change the spatial cues and stereo imaging, not the overall sound quality (noise floor etc). When digital data is sent, it's sent with same clarity independent of the device sending it (proprietary formats notwithstanding)
If you can, you will be far better off using the receiver's DAC by running HDMI or optical/coaxial digital to your receiver, rather than run finicky, long, poorly shielded unbalanced cables from ZXR to receiver. This is because the receiver does an extra ADC, which means analog to digital conversion, before it processes the sound and applies any adjustments you've made on the receiver's side, and then it converts it to analog again. This doesn't really destroy the quality half as much, as the long unbalanced analog connection with no good shielding that is also subjectable to ground loops, and inducted interference (buzzing, noise, hums, cracks..)