Without the users table the posts would never show up since the users that they are tied to wouldn't be there, so the posts just wouldn't display at all. Plus I don't think you have the topics table either which again isn't good.
So it's pretty important to get all of the tables in place. You could do a full install, drop all of the tables and then import the full backup when you have it, but it's probably best to just get the full backup, since it's somewhat wasted time to do a full install first.
