Can AWS DocumentDB have something similar to a hot partitioning issue?

1/ I assume that the question is about the _id field. Yes, DocumentDB allows setting custom ObjectId values in this field as long as the values are unique for each document in a collection.

2/ DocumentDB does not partition data. All writes go through the primary instance in the cluster and any primary key can be read from any of the read replicas. You will not have hot keys in the same sense as other products like DynamoDB and S3.

There are other considerations that you should keep in mind to maintain good performance. See https://docs.aws.amazon.com/documentdb/latest/developerguide/best_practices.html