once you receive your Odyssey Audio monos just unscrew & remove the top lid & take a look inside to see how the RCA & XLR inputs are connected. I'm reasonably confident that the XLR connector is connected to the RCA connector with a short piece of wire: hot of XLR to center pin of RCA & minus of XLR to ground of RCA. The 3rd pin of the XLR will not be connected at all. You'll probably also see that the cable carrying the music signal to the amplifier is connected to the RCA connector & not to the XLR connector. If this is the case (& I'm expecting this to be the case) you'll know exactly which type of connector is being favoured (& it should be the RCA).
So, in this particular design you will be fooling yourself to think that an XLR-based cable is actually giving you a XLR sort of connection - it is not. All you have is signal & ground on the 2 wires of the XLR connector just like the RCA cable. So, you are not going to get the benefits of an XLR-based cable (like they do in long cable runs in the home & studio environment).
So, in this particular design you will be fooling yourself to think that an XLR-based cable is actually giving you a XLR sort of connection - it is not. All you have is signal & ground on the 2 wires of the XLR connector just like the RCA cable. So, you are not going to get the benefits of an XLR-based cable (like they do in long cable runs in the home & studio environment).