[mwebb]

depending on the system
there are many things used to determine when to go into "closed loop"

but
none of them can over ride the need for the 02 sensor to report to the ECM
until the 02 sensor begins to cycle , the system does not know how to make a correction to real time fuel trim because there is no "feedback" if no feed back
...
the system can not be in "closed loop" ,
the old POS GM TBi systems will revert to open loop at idle because the 02 sensors did not have heaters , they would go to sleep and not report conditions back to the ECM so the ECM had no "feedback" upon which to make decisions about what to correct .

that is what "closed loop" is , real time corrections to measured conditions , there can be no "closed Loop" if conditions to be controlled can not be measured .

most newer systems are in closed loop in under 1 minute from cold start , even if ECT and IAT says system is cold.
they enter closed loop when the front AFR or 02 sensor begins reporting and they begin to report the second they reach operating temperature

which is why

all new systems have ECM managed heaters on the AFR sensors (front) and 02 sensors (rear)

so
on newer systems with heated AFR or 02 sensors ...
warm / hot air to the intake has zero effect on time to closed loop from cold start.
none the less WAI does have other benefits related to
Fuel Economy