It's a bit complicated, I'm afraid...
The main thing to bear in mind is that a DAC only accepts a digital signal (and converts it to an analogue signal for your amp).
If you are currently playing the iPod Touch through a phono lead into your amp, yes an external DAC would improve the sound of the iPod. BUT you'd need a DIGITAL iPod dock to get the digital signal out of the iPod into the DAC. Cambridge do one at 150 quid. Or...get an iPod dock with analogue out (which has a built-in DAC). That would improve on the phono lead, but not be as good as a digital dock plus external DAC.
Same thing with the tuner, does it have a digital output or just analogue? If there's no digital out, you can't plug it into a DAC.
Overall, it's worth noting that the DAC inside your CD player is almost identical to the DAC in the Dacmagic, so if you fed the Dacmagic from your CD player, there would be no improvement at all, in fact it could be slightly worse. Other DACs in the same price range as the DM might offer a slightly different presentation, but no night-and-day improvement.
It's a shame your CD player doesn't have an iPod input like the Marantz 6003/6004, otherwise you could just plug it in and feed the signal from the iPod to the DAC inside the CD player.
I think the main reason to get a DAC is if you want to use a PC or streamer as your source instead of CDs, or if you don't already have a reasonable CD player and want to spin discs from a DVD player (or Playstation or something!) that you already have.