Mounting a rad would cause no advantage - let's say I have 25°C room temp here in Summer - so the rad is not able to cool down the water sub room temp, that's the reason the chiller does all the work.
Regarding to Your 2nd question, when my system is OCed near limit so that I need really cold water I can set off the chiller and have cold water for almost one hour - but I forgot to insulate the tank, if You do that with some Armaflex the cold will last longer.
When my system is not OCed I can run it without switching on the chiller.
My current E8400 runs 9x333 @ 0.984 Vcore - this is stable even with water temp = room temp.
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