@ML-1722 Apologies for the delay response!
No, the write will not fail if one AZ is unavailable documentation states "If an availability zone is temporarily unavailable, the operation returns successfully after the data is written to all available zones." In this case the available zones would be the two-remaining available AZs. We also include a chart lower in the documentation that explains each scenario a storage account is protected from based on the redundancy variation.
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