Hello @Sahil Mehta ,
Thanks for the question and using MS Q&A platform.
As we understand the ask here is how to refresh AAS with the firewall set ., please do let us know if its not accurate.
You are correct AAS is very tightly coupled with the AAD and at this time you do not have anything like SQL accounts .
The firwall which is set on the AAS does that allow you to other Azure service to interacts with AAS ? One way which you can try is to user ADF . The below link which calls out the steps in great detail .
https://www.techtalkcorner.com/azure-data-factory-refresh-analysis-services/
Please do let me how it goes .
Thanks
Himanshu