I was looking into this myself and from what I understand, it is currently not possible to directly create this rule, but I think it should be doable with a different approach.
Instead of requiring a custom rule that disables merging (which doesn't exist today), you could make it so that the PR requires review from a specific IAM user. With that, you could probably use a fixed "build" user, and fire an automatic approval request for the PR once the build finishes successfully. This will in turn "approve" that rule in the PR and allow it to be merged after the build succeeds.
Since approval can be done via the CLI interface, I'm sure it should also be possible via API. For example, you could use this API to automatically mark any given PR as approved by the calling user, then ensure the service that is calling it is the same user registered in the "build" approval template.
Besides the HTTP WebApi, there are also other ways to call into these CodeCommit actions, like the AWS SDK library (C# example: https://www.nuget.org/packages/AWSSDK.CodeCommit/).