At least this idea is inventive and a little bizarre - much better than skipping tracks on your CD player! If I had a spare cart laying around I might try it.
Wouldn't the CD player output be too hot for the cartridge? Hmmm.
Now, what if you reversed the sources and played a turtable into a CD player? Would you get clean digital sound then?

If you really wanna color the sound of your CDP I might suggest running it through a SansAmp Bass DI pedal (well, two of them actually) this will get you a very tubey, analog tone for sure, no joke. And since modding pro audio gear is all the rage now, you'll be set!