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"AWS Cloud9 is a cloud-based integrated development environment (IDE) that lets you write, run, and debug your code with just a browser."

I would say no.

You can easily SSH to a Cloud9 instance, so it would satisfy the criteria given.

Alternatively, one can launch a custom AMI in EC2 to do whatever they want.

Multiple solutions already exist for the given problem, therefore yet another AWS service seems unnecessary.

Except that Cloud9 requires an EC2 instance and associated spend, whereas CloudShell is free.