Hi @FirehouseCoffee ,
Not always, that is up to the app developer. Things like webhooks are deleted by Shopify but the app developer is responsible for theme code and assets that have been uploaded. There are common places like themes/snippets for example where you may find the actual code but you will also want to check your actual theme.liquid for the includes to those files.
If an app inserts code into your template, that app must support the uninstall function on its dashboard. Some apps support this, on the dashboard of the app will have a "remove template" button, click on it and then back to Shopify's dashboard to uninstall the app, if not, you have to manually remove it only. Because when you uninstall the app in Shopify's dashboard, at that time the app no longer has access to your template, they cannot remove it even if they want to.