Does Commerce Health change anything on my site?

No. Every diagnostic and every PRO monitor only reads your site’s configuration and events. They never modify settings, content, products, orders or WooCommerce data.

The one exception is the Test order tool, which you start yourself. It creates a private test product and a clearly marked test order, only when you press its button, or when you switch on PRO’s scheduled test orders. See What test orders do to your store.

The plugin does write to its own storage (scan results, issues and, for PRO, monitoring samples) in your WordPress database. By default that data is kept if you uninstall; see Settings for the option to remove it.