According to Amazon AWS
Customers may use any AWS service in an account designated as a HIPAA
account, but they should only process, store and transmit PHI in the
HIPAA-eligible services defined in the BAA. There are ten
HIPAA-eligible services today, including AWS Snowball, Amazon
DynamoDB, Amazon EBS, Amazon EC2, Amazon Elastic MapReduce (EMR),
Amazon Elastic Load Balancing (ELB), Amazon Glacier, Amazon Relational
Database Service (RDS) [MySQL, Oracle, and PostgreSQL engines only],
Amazon Aurora [MySQL-compatible edition only], Amazon Redshift, and
This means that as long as you are not storing or transmitting PHI in SQS, just the information about where this PHI is being stored - you probably can pass an audit reg. HIPAA compliance.
In the architecture you describe, the SQS queue does not need to include any PHI content. This would make it comply with the above statement.
More information about HIPAA compliance on AWS is available in this whitepaper from January 2017 - https://d0.awsstatic.com/whitepapers/compliance/AWS_HIPAA_Compliance_Whitepaper.pdf
Specifically SQS is mentioned and explained in the HIPAA FAQ - https://aws.amazon.com/blogs/security/frequently-asked-questions-about-hipaa-compliance-in-the-aws-cloud-part-two/.
update: As of May 1st 2017, SQS is now HIPAA compliant. https://aws.amazon.com/about-aws/whats-new/2017/05/amazon-simple-queue-service-sqs-is-now-a-hipaa-eligible-service/