I recently helped a colleague upgrade her system. I put the new integrated amp and speakers in place, a Creek A50iR and Soliloquy 5.0's, but decided to plug in the mid-priced Sony 5-disc changer she already had since we knew it was working and I wanted to introduce the variables one at a time if possible.
She put in a CD and music came out, but the sound was so bad that I was scared I'd really screwed something up or that the new gear we'd spent a lot of time picking had turned out to be a horrible mismatch. I nervously shut things down, checked all the connections and tried again. Same thing, thin, bright and extremely irritating. So, I nervously unpacked the Philips 963 player that was to serve for both CD and DVD playback, plugged it in and put in the same CD.
The difference was remarkable, with the Philips, her system sounded just as I'd hoped and she was absolutely thrilled with the sound. Still, we left the changer in place because she entertains a lot and reasoned the fidelity really wouldn't matter to a room full of people at a party.
Keeping the changer for convenience and adding a decent single player of some kind for critical listening makes a lot of sense. With some excellent players available used in the $300-500 range, it might not be worth your trouble to experiment with the external DAC and you could choose convenience or fidelity with the flick of an input switch.