YES. It is perfectly safe to do so, and you should update the database whenever prompted to do so.
If you log in to the backend of your site and see a purple button asking you to update the WooCommerce database, you should click it. It will simply improve the performance of your site's online store. Teesnap does not update this for you.
What About Installing the WooCommerce Admin Plugin?
If you see an additional purple button prompting you to install the WooCommerce Admin plugin, you can simply click "Dismiss."
We do not recommend installing this plugin, as it is currently in beta mode, does not add any needed functionality to your online store and adds unnecessary bloat to your site's database. See more about the WooCommerce Admin plugin here: https://mainwp.com/do-not-use-the-woocommerce-admin-plugin-on-your-child-site/