Tickfight, No if your CD player is a Wadia or a Pioneer or a teac, using the same mechanism(transport) then you would be suprised how similar used as just your CD reader(transport) they can be... I have tested this, When you purchase some of the higher cost players you are paying for the metal work, fancy jacks, Displays, and even sometimes the IEC detachable plug, and yes your Wadia unit, or Krell whoever is simply a very modified Sony, Teac, Pioneer, or phillips transport. So your education should start with Who uses the best transport in stock models, like the VRS? teac, The pioneer stable platter, Sony whatever.
I have directly owned and compared a Wadia and pioneer using the same transport, and even Logic system(board with all the functions on it), and even the Same remote(just silk screened over with Wadia's logo, and guess what? They were EXTREMLY similar when used as a transport only, however the Wadia blew away the pioneer if using the internal DAC and better Chassis damping and power cord.
Also I owned a Sony top player with the transport they use in some Krell machines, and again Near identicle using the digital out.. So even if a cheap plastic player is using a hi quality transport it should be pretty good even in comparison to a couple thousand dollar more player using the same, unless it has Extensive power supply upgrades, and most in the 300-3000.00 range do not.
So put most your money into the Seperate DAC first, find what you like, then Experiment with a 200.00 transport and a 4000.00 transport and make your decision on how much is enough. But guarantee that a Transport will make some big difference with the DAC it is matched too, I found some transports sound a little soft or fuzzy, and some sound deeper with better detail and bass on the same DAC, so they will be effective to the end result, but find a good dac first I say, and transports in all these machines are made by Sony, Teac, phillips for the most part today anyway from my understanding.