Assuming you have a 100% full radiator any fluid in the overflow does nothing to aid cooling.
If you do not have an overflow, as stated before, the rad will find its own level. Agreeded the amount of coolant in the rad will be less, but it will not have any effect on the ability of the rad to cool the engine, it is just an air gap at the top of the rad. The pump is not going to suck air etc.