OrderlyEmails does need to be installed in case you need to make adjustments to your email designs through the app editor or when our emails templates code is updated to comply with Shopify requirements whenever they release any updates.
Additionally, a few of the more "advanced" features require the app to be installed to continue working correctly.
The Recommended products section: They would stop updating if you uninstall the app.
The Email click tracking: The emails push conversion and tracking data to your Shopify reports. This will stop working if you uninstall OrderlyEmail.
Other than that, everything else would continue working. OrderlyEmails does not actually send any emails itself nor trigger the emails to be sent.
The app is a design tool that upgrades the emails that Shopify is sending for your store. Therefore your store continues to work exactly the same as before, just now with much better email designs.