Yes... if you do a FRESH upload to your public_html folder, then you are well-advised to DELETE the copies in all sub-folders.
If you MOVE the original install up to your root (public_html) directory, then you MUST change the path settings in your configure.php files.
There are TWO of these, and you must not confuse them with each other.
includes\configure.php
admin\includes\configure.php
There is LOTS of advice on the forum regarding these important files, so read up about what they do, and how to configure them.
Also, do not forget to REMOVE the install directory when the install is complete, and you must also set your configure.php files to either 644 or 444 CHMOD permissions.
If you fail to do this, you will get big red error messages in your shop header!
If you set CHMOD to 644 and you still get the error bars, then use 444.
File editing should be done with a good text editor, such as CRIMSON editor (free on the www - search google). Don't use any c-panel editors as they are known to corrupt php code.
Always DOWNLOAD a copy of php files to your hard drive, edit them on your local machine, then FTP back to the server.
You would do well to learn about the OVER-RIDES system that zencart uses.