yes, I believe you would have to

You can do a lot with symlinks (assuming you're running a Linux/Unix server), meaning that you'd only have to keep one set of files for the most part. I don't do multiple board hosting, but as I have a lot of themes I use symlinks for the admin section directories as this vastly simplifies installing patches. You could just keep the majority of the files in one central location and symlink from each virtual host set up for each board.

It all depends how good you are with PHP, if you can script the rest of the board creation process and config.php file, then you could probably set up multiple boards reasonably easily.

I decided to copy just connection php file for every customer i get. Tell me if this is a good idea?