I've just posted another interesting question regarding the LKM's position in the kernel space, and it looks something similiar to this.
As far as i know, the sys_init_module allocates the kernel memory to hold a module by utilizing the vmalloc, and then it copies the module text into that memory region, resolves the kernel reference in the module via the kernel symbol table and also register its new exported symbols. As for the range of the sysmap, i am not so sure, maybe others can give a comment.
Regards
Jason