WICED modules typically come with a Cortex M3/M4 MCU that is internal to the module. The Linux i.MX6 based modules are radio only (no internal MPU/MCU), but work with an ARM 9 class processor from NXP/Freescale.
Higher level software would need to be running on the module to accept AT commands.
The uC that is internal to most WICED Modules already runs a TCP/IP Stack and an RTOS. WICED is designed to work with our eval boards and partner modules with internal MCU. With partner modules, the partner themselves would need to provide a platform file for that particular module which would then be used within the SDK.
The radio only modules available from some module providers can be used with WICED and external MCUs, but the module partner normally has higher engagement criteria for these modules as the support burden is greater.
If you haven't already done so, you may want to take a look at the IoT Solutions Guide