This is definitely doable. We have a number of customers using strictly WICED Wi-Fi Driver (WWD) plugged into their existing framework and applications. WWD has clearly defined interfaces which allows you select RTOS, network stack, and platform of your choice.
One other option is to consider Inventek's AT Command for Packet Bypass Mode (PBM). The PBM sends the received Ethernet packet directly to the host interface bypassing the module’s TCP/IP Stack. Currently UART and USB HID interfaces are supported. The SPI interface becomes a little more difficult because this is a synchronous interface developed for high throughput. However it could be adopted for bypass mode if SPI is the only I/O available. Contact firstname.lastname@example.org with further questions.
This may be doable, but it's certainly not easy or straight forward. Is there any relevant documentation or application note? I'm trying to use the WWD\Application project as a starting point but not making much progress. I started by trying to integrate one source file into my existing project. It's nearly impossible. There are at least 50 nested include files, almost every one of which requires its own path, I may end up gathering all the include files into a single directory. Needless to say, this doesn't 'feel' right. I don't think I'm headed in the right direction. Can anyone offer some specifics?