Yes that option will work.  However you can only have on file marked for efile at a time, so you would file the federal and whatever states you attached to the first return.  After they are all accepted you would unmark them for efile to remove them from the EF center homebase view, and then mark the second set for efile.

I would recommend doing them in smaller batches than 16 states though, maybe 8 states per file.