Your headunit is the brains of your stereo. You buy crap and thats what you get. The best way to get nice clean sound though is to totally bypass the headunits internal amp and run your components with external ones. Those too must be of decent quality. For a headunit I would recommend Kenwood. The one I have sounds great. However, it depends on your budget and preference. Pioneer is ok but as I said I prefer kenwood. Anyway, the answer to your question is yes, your headunit does make a difference in the sound quality of your system.
In my 2002 Jetta I have an Xtant "A" series 4004 amplifier hooked up to the factory head unit. Xtant's input section allows for a powered signal without the use of a line level converter or any of that other crap. Just solder RCA ends on to the speaker leads and plug it in. Anyway, I measured the input voltage and it was over five volts!!! It sounds really good. Just my 2 cents.