I do not think it can work, as 1 cache file is generated for each single page no matter what device is used to generate it. I have never looked how those mobile themes works, but I assume based on some indicators it switch standard theme to mobile one. Until there is no parameter passed, plugin will not be able to recognize it is different theme. Generally I do not think it can work with 2 themes securely.
//Edit: It is actually not mobile theme, it is plugin.