Is there any way to have two AWS Orgs coexisting?

Yes, it's possible to have multiple AWS Organizations, but not within the same AWS account. An AWS account can only be part of one organization at a time - either as a management account or as a member account.

For your specific use case of testing AWS Organization setup automation, you have a few options:

1. Create a new AWS account outside your existing organization specifically for testing your product. This is the cleanest approach as it gives you a fresh environment to work with.

2. Use your existing organization for testing if you can create a separate Organizational Unit (OU) for test purposes. However, this won't let you test the actual organization creation process.

3. If you've acquired an entity with its own organization, you could temporarily use that separate organization for testing before eventually merging it with your main organization.

The most straightforward solution for your product testing needs would indeed be creating a new standalone AWS account. This approach ensures you can test the complete organization setup process without affecting your existing organization structure.

Remember that when moving accounts between organizations, an account must temporarily become a standalone account with valid billing information before it can join another organization.
Sources
Multiple organizations - Organizing Your AWS Environment Using Multiple Accounts
Account stuck in root organization | AWS re:Post
Move an account to AWS Org from another Org | AWS re:Post
How to add and manage AWS organization in AWS partner Master payer | AWS re:Post