Roughly, in terms of integrating a SDIO based Laird module in to Android, what software of the Linux world is usable and what needs to be Android specific?

The same driver is used for both as Android uses the Linux kernel.  However it is the userspace that is very different. Integration with Android requires assurance that everything in Android is setup to work with the desired hardware driver. Under Android, radio specific commands are sent via the supplicant. There is a library that is linked into the supplicant for each wireless driver to allow for vendor specific commands to be sent. This is would have to be made avaialble for each combination of WiFi module and Android version.