Functions relies on Azure Storage for operations such as managing triggers and logging function executions. For example, in case of timer trigger function, it stores information about last execution time along with other meta information and synchronization related information.
The Azure blob storage is used to maintain state and function keys.
The Table storage in storage account is used to store metrices related to function execution along with other information.
You can connect to the function app's storage account using Azure storage explorer to check these details to get an idea.
Therefore, it is possible that your functions might continue to execute (especially http trigger function) even when you disconnect the storage account. However, for smooth functioning of the app and for it to be triggered correctly, it is required to have a general-purpose Azure Storage account that supports Blob, Queue, and Table storage.
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