The esc does not draw the amps, the motor does. The esc just controls the flow of power from battery to motor. You should get a more than 6 min just based on experiance. Off road guys run 4600 shorties with 6.5/7.5 motors and make 10 minute mains. Run time is going to depend on gearing, time spent at full throttle and braking. Excessive wheel spin will also cause a decrease in runtime, as does a heavy car and a bound up drivetrain.
But may I ask if your that new to the RC scene that you are unsure of run time, why would you get one of the fasfest motors you can buy right from the start?
Tamiya EVO 6 with EXOSIX conversion
tamiya box stock Mini (M05)
SMC - Motiv motors - Savox - Spectrum - Exotek.
The brighter the picture, the darker the negative. USVTA member #112