Managed updates feature in elastic beanstalk

In short yes - see here

"Releases patch, minor, and major updates of operating system (OS), runtime, application server, and web server components typically within 30 days of their availability. Elastic Beanstalk is responsible for creating updates to Elastic Beanstalk components that are present on its supported platform versions. All other updates come directly from their suppliers (owners or community)."

There is no reason you cannot additionally configure SSM Patch Manager for beanstalk managed instances to double check these instances are meeting your patch baselines