I don't know

In my case, I just compile the module, make install, depmod, env-update, than it's ready for modprobing

I don't actually know if env-update is necessary for me, but since I compile it so infrequently, I don't really want to test
Also, you want to install the custom module after you've installed the kernel's own modules with make modules_install, or it'll get deleted. You might also want to check that the /usr/src/linux symlink is pointing to the right kernel sources folder when you compile/install the other module, so it gets installed to the right place for the correct kernel version.