Aurora's read replicas share the underlying storage that the primary uses, so AWS claims that there's no data loss on failover. They also claim -- and I've never heard anyone say they were wrong -- that Aurora failovers take less than a minute. So the pain should be limited to under a minute of lost writes, which most applications can handle (with an error). It can still be painful depending on the application.
See here for more info: https://aws.amazon.com/rds/aurora/faqs/#high-availability-an...