Wordpress Plugin Upgrade Hook Function
The Options API is using the global $wpdb, make sure you have that declared before using any function like add_option or get_option.
Also acording to the WordPress Codex, you will see no changes when you use add_option($option, $value, $deprecated, $autoload) if you already have a value for that option:
Note:
add_optionuses get_option to determine whether the option already exists, and sinceget_optionreturns false as the default value, if you set an option to false in the database (e.g. viaupdate_option($option_name, false)), then a subsequent call toadd_optionwill change the value, because it will seem toadd_optionthat the option does not exist.
You can use the Options API anywhere in your plugin as log as you load $wpdb.
Also I'd recommend using update_option instead of add_option as it is able to create new options but won't return false in case an option already exists, it will simply overwrite it.