Hello, (all the following tested on test2.wikipedia.org, version 1.21wmf7)
it is possible to create modules in subpage of a module (i.e. Module:Taxobox-fr/tools).
It can be included from the "main" module and it is usable, but wikimedia software fails to detect modifications to the submodule. So a change in the submodule is not visible from articles that use the main module (via the template call).
But if I perform a change in the main module all changes are visible: the one in the main module and those performed previously in the submodule.
Maybe it is not a good idea to use subpages for modules, but in my opinion modules that are fully dedicated to give functions to one module are better here.
Whatever if using submodule is not the good way the software should prevent users to create them (and to effectively use them).
If it is allowed this "cache" problem should be corrected.