Should I add a DAC ?

You would have to purchase a well designed dac in the $1200-1500 list price range before you'd start hearing substantive improvements, assuming the rest of the system is revealing enough.

I concur with the prior responses. Underneath the hood of many DACs is the same hardware that is in your CD player. You would have to spend goofy money to get an improvement worth writing home about. I think the $1200-1500 figure in the previous post may be low.
Demo some good speaker cables if you can, or upgrade speakers, or improve the room acoustics.

Bel Canto DAC 1.1 at under $600 will substantially improve the sound of that player - this is just one possibility. The above cost estimates for DACs to improve on the Music Hall don't match my experiences with that unit. I wouldn't expect most used DACs in the $400 or below range to do you much good, however - but a notch or two above that ($500-$750 even), you'll find several models that can substantially improve on its sound.

The CI in particular I would not worry about - you'd notice differences, but not all of them "better"... it's a nice unit, but very entry-level. I've owned it as well and would not recommend it to improve on your player.

Keep in mind, just because a DAC may have similar "hardware" (DAC chips etc.) as your player, its likely that its analog output stage is built to a higher standard as a standalone unit, and will be packing a better power supply etc. These differences can produce substantial performance gains.

The Music-Hall is a "giant-killer" to some degree, but I find that in their enthusiasm for the product, people can overstate that accolade. A decent mid-priced DAC can certainly help this unit achieve better performance.

Mwilson's idea to add a more expensive dac you purchase used makes the most economic sense to me. Dacs depreciate rather radipdly and you can buy a used one for $500-600 that will make a substantial improvement. The Bel Canto 1.1 is often available and would be a step up in performance. Elizabeth is right about needing to spend another $100 for a cable. The Sterovox HDVX is about the best value ($100)going now I think. As to her assertion not to dac, that's a personal value judgement. I happen to think there are substantial gains to be made and it is worth it. You might agree with her though and think the money is better spent on something else. It's so subjective, these questions of value.