Do I need a DAC?

No, unless you're dissatisfied with the way the system sounds presently.

shouldn't need 3 DAC's...though the DAC in an integrated is not always so great...and the DAC in some CD players is not connectable to other sources...shop carefully

No, but you may prefer one over the other so try both.   I have my disc player hooked up to my pre and DAC.   One analog and the other coax digital 

Yes you absolutely do need an external DAC to "improve" sound. At what price point, ain't no telling. 

Without you going through it.

Try what you currently own. If it sounds good to you,you have arrived. If you feel there is something missing,then try something else.  Build your system to fit your tastes and desires. This is a hobby,not a contest. Enjoy the music first and foremost.