How to add/change a value of $wpdb property/var?

Yep, just declare global $wpdb early enough and modify its fields. Codex docs for add_metadata() say exactly that:

Note that you will also have to register the table with the $wpdb object in order for it to work. Simply add the following to WordPress’ init hook (or at least before you attempt to use any custom metadata functions).

global $wpdb;
$wpdb->termmeta = $wpdb->prefix.'termmeta';