DAC or CD Player. Help!

Synergy is about the most useless audio platitude I can imagine. I'm not trying to be rude, seriously, but it's so absolutely objective as to be absurd. It's like saying "get the best white base you can" when buying paint.

Forgot the question :) .. if the transport isn't shite (most middling+ CD players) then I'd say the DAC. Rarely, if ever, the cables. On both the desktop and main system I use Cambridge players, and both run the signal to a DAC. A NAD 1050 and Arcam irDAC. I run them that way because I'm convinced through trial and error that they sound better dumping their 1 and 0s to the aftermarket DACs. Having said that, when I was using a 1st generation DAC Magic (Cambridge) I couldn't hear enough difference to matter. In fact, that DAC sounded brighter in comparison to the CD player alone.

All matters including cable.  Synergy is important.  In case of digital connection it will be output impedance of CDP, input impedance of the DAC and characteristic impedance of the cable.  It will also be length of the cable, slew rate of the CDP etc.  It is a system thing.

RSA,

it all matters!

This isn't very complicated. CD players are just three components built into one box, the transport that picks up the bits from the disc, the built-in DAC (digital to analog converter) and the analog output stage that sends a signal to the preamp or integrated amp. 

They're all important, as others have mentioned, so the question about using a separate DAC really comes down, sonically, to whether the DAC and the analog output stage in your CD player are better than an external DAC and its analog output stage. 

But, one of the big advantages of using an external DAC and relying only on the player for sending the bits to the DAC is that the transport in a CD player will always eventually fail.

They are mechanical devices, like the tires on your car, and they have a limited lifespan. Replacing the transport in a quality CD player can cost more than what you paid for it originally.

DACs are being improved upon daily. Good ones are not that expensive and you're much better set up for the future of music reproduction if you make the move now.