The phones will sound different, no doubt. But I personally dont want to let my headphones be any sort of deciding factor for which CD player I get. In my case, the headphones cost me ~$330. Even at $1000, its not something I'd want to place emphasis on, if I was looking at any source $3k and up.
My general attitude is, give me something as neutral yet natural as possible, with good tone and data retrieval, mico and macro. The headphones will add their own sound on it, but I just dont see that as a deciding factor.
I know most disagree, and strive for synergy, but I'll probably be running god-knows-what brand of speakers with the same CD player eventually, using god-knows-what amp. I want a CD player that will work with anything. Maybe thats a bit lofty though.
I suppose if I were looking for slightly cheaper sources, I may view it a bit differently.