Can GraphQL be deployed to Elastic Beanstalk?

Customer wants to deploy an existing GraphQL application to AWS. This application will connect to an existing RDS MySQL database and a couple of on-premises databases. Once it's in AWS, the applications that use it will also be migrated to AWS.

I told them about AppSync, even though they'd have to use Lambda to connect to their non-Aurora/DynamoDB databases. They asked whether they could use ElasticBeanstalk to deploy it to EC2s that auto-scale with an ELB, but I couldn't find a definitive yes/no. I found a few blog posts that seemed to say EB doesn't support GraphQL, but they were relatively old. They are interested in using the Code suite of services, and CodeDeploy can deploy auto-scaled EC2 instances, but if they can do it through EB or CodeStar that would be even better.

Any help would be greatly appreciated!