AWS Directory Service

Yes, it is possible using a combination of AWS services.

However it's more of a Microsoft AD question than an AWS Managed AD question.

If your main concern is DR and not willing to move the AD into the cloud, then one option you have is to use AWS Elastic Disaster Recovery (DRS), the next generation of CloudEndure DR. What it does is to have a block level replication of your on-prem AD servers into the cloud and you can launch it when you needed to during an incident. In that approach the AD controllers in the cloud will act very similar to your on-prem AD. There might be some down time when you spining up new AD servers on the cloud, but it should be minimal, and your users can reconnect as normal after that.

You also have the options to use AWS Managed AD. However, in that case you it would be a different forest, which might not address your DR needs.

Lastly you had the option to host your AD on EC2 and add them as domain controllers to your existing AD.

I know many customers are cost conscious, but I do recommend you think about migrate the Active Directory completely to the cloud. Using AWS Managed AD cross region replication, you have a fully managed AD solution that can help you achieve the SLAs you are looking for.