You can put the ZIP files into
/install/module/ or /install/skin/
then call your website/install/install.aspx?mode=installresources and DNN will install any ZIP files in the various sub folders of the install directory.
As for syncing across multiple webservers, that is something you have to configure. I believe DNN Corp still recommends using a NAS for file storage, all web servers pointing to the same NAS, instead of doing file synchronization as DNN itself won't do syncing.