AC cord for cdp

I just ordered a Dacmagic from Cambridge Audio. The manual states not to upgrade the power cord, which is a 12 volt pin. If this is the case, would upgrading my ac cord on my cdp make any difference? Currently my cdp doesn't have a removable ac cord, but I was planning on upgrading it to one that did. However if won't make any difference I won't spend the money on a new cord. I'll hang up and listen to your responses now. Thanks.
So you are going to use the CDP as a transport with the DacMagic? Or are you going to use the CDP as a stand alone digital transport and DAC, and use the Cambridge for your computer or iPod?

If it is the former, then I say "probably" a new cord for your CDP would make a difference. If it the latter, then i would say "definitely" a new cord would make a difference.
I plan on ussing the dac for my computer, but was going to try it out with my cdp as well. I'll experiment and see what happens. Thanks for your responses.