it has to on closed loop control as the sensor is non linear and essentially is just a switch so that the ecu knows it's either rich or lean so it cycles around that point.

adjusting your global modifier will affect the whole range whilst out of closed loop (with attendant potential problems as already mentioned by Rick), but as you seem to understand already there should be enough adjustment available by the closed loop control for it to be able to stay under closed loop control around stoich at idle and cruise.