Hi Niggie Anwar (IT Services) - Thanks for reaching out.
Based on the documentation, access to a storage account from trusted services takes the highest precedence over other network access restrictions.
I further notice API Management Service is part of trusted service list.
So ideally, this should tend to work. I would recommend testing it out once and in case there are any exception observed, you can raise a support ticket for further deeper investigation of the logs ahead.
Hope that helps!
Let me know if there are any further queries/concerns, will be glad to assist.
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