In standard post mix system installs, bibs are never chilled. It causes inconsistent brix due to the change in viscosity from the bib to the valve....especially during high usage times....but these are usually significant line runs from a back room to the fountain unit.
If you are using a flowjet or sureflow, co2 driven pump it will pump the syrup chilled....you can adjust the co2 pressure up as needed....i think they top out at 80-90psi or so...i can't remember right now....I can check at work.
The key to good soda is having the temp of the mixture pouring out of the valve to be at or under 38 degrees, measured in a glass with no ice. The warmer it is, the flatter it will taste....even once poured on ice.
The output pressure of the carbonator can be anywhere from 75 to 100 psi depending on your settings....just an fyi...concerning the corny keg pressure relief valve....it may be close....there have been some others that have tried this set up....but I have not heard back on how they turned out.
(co2 pressure needs to be at least 10psi higher than your max water supply pressure)
hope this helps,