yes, you can install Power Store on your local server, then use FTP to upload it.
You will not need to re run the power store install when you upload it to the remote server, you will need to edit the database connection file to use the details for connecting to the remote database. you will also need to use PHPMyAdmin to export the power store database tables then import them to the database on the remote server.
I recommend setting up power store in subdirectory of your local testing server:
and uploading it to the same subdirectory on your live site: