As the PWM uses a dedicated internal module it is not so reliant on the firmware to keep the PWM pulse stream operating.
Therefore in general PWM will keep operating in the background.
The PICAXE hardware (Microchip PIC) has several hardware timers, some of which are used for PWM control. Once configured by your software and PICAXE's firmware, the PWM functionality is performed completely in dedicated hardware, although it can be shut down in some hibernation-type conditions.