I've done something similar, it works but sound quality varies, which I think was due to impedance mis-matching.
I've used PS HCA-2 which is balanced and have both RCA and XLR inputs. I've hooked up my Wadia 301 using XLR to XLR of HCA-2 and front L/R pre-outs from my Parasound processor using RCA to RCA of HCA-2. Just turned off the Parasound when I was using the Wadia, worked perfect.
The difference I've noticed was that if I don't turn off the Parasound and switch the source to a input which is not hooked up and play the cd player, sound level, resolution, bass evrything was higher. But if I turn it off and just use the cd player, sound level just drop and I've increase the volume level on Wadia.
I ended up getting a pre-amp with HT bypass and everything is perfect now. I run the Wadia with full volume through the pre-amp, get bigger soundstage, better resolution. I may lose some detail as Wadia is better in detail if you run direct to an amp.
I think you should try a pre-amp with HT bypass like PS PCA-2, ML 38/380. There may be others, I sure someone can provide you with some advice. Try to audition using a pre-amp before you buy a new cd player.