Had the same question when I got my Sumiko BP#2, which is only 2.5mv. I am running a Thorens 124 (which is not the quietest table on earth), through a MA6200, which is essentially the same pre as the C32. Although I do have to turn the volume knob higher than most carts to get the volume I want, the phono stage is near quiet with only the slightest hint of "air". The phono pre in your C220 is light years better than the one in my 6200, so it should be DEAD quiet.
I did however have an issue with my Fisher 500c (here's the tube comparison) where I could hear the "hum" on a low output cart (had to turn th volume up like you). I swapped my Grado (4.5mv which is high but wasn't high enough to get over the noise) with a Pickering V-15 (5.5mv) and the noise was much quieter as I had that much more signal. I then later swapped the original Telefunken tubes with a set of new Mullards and the noise is now almost silent. The Tele's I had were microphonic and the new Mullards (I bought a matched/low micorphonic set from Tube Depot), solved the problem. I also got a set of vintage Mullard 12ax7's in another tube reciever and compared them with the new Mullards, and dare I say the new ones are pretty close for 1/10 the price.
I say you need to swap your factory Chinese tubes with a good set of NOS 12ax7's (I vote for the vintage Mullards as they are the sweetest phono tubes I have ever heard...at $150each!!) The new soviet tubes from companies like EH or Sovtek (own the new Mullard label) are very good if you get them from a US importer that screens them all for QC (like Tube Depot...no affil)....well worth the gamble at those prices IMO.
James R.