Yes, if you resided in AZ for the full year and received a pension from IL it would be includable in your AZ income and you would file an AZ resident return.
If you moved in to AZ from another state you would apportion the income when you file an AZ Part-year/non-resident Return.
Below is the link to the AZ Department of Revenue showing what is and is not taxable income for AZ purposes.
AZ Dept of Revenue
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