I have used aws-nuke to manage my AWS organization accounts. You can definitely use cross-account roles for the task assuming that you already can run aws-nuke on your resources in your AWS account.
What you can do inside your AWS account, you can do with cross-account roles except for a handful of AWS actions. The only issue will be the AWS cross-organization role will have to be too much permission and that is risky. AWS-nuke documentation says, such tool for AWS-nuke is very risky and destructive!
Linking AWS accounts via AWS Organization allows you to consolidate billing, use Service Control Policies, etc. It doesn't actually give any more capability than what you can do with Cross-Account Roles. You still would need to use those as SCP actually doesn't give you permission that IAM doesn't give you.
So to answer your question, would you be able to do it with AWS Organizations?
Yes, if you use cross-account AWS role.
Would you be able to do it with other non-members too?
Yes, with cross-account roles. I am emphasizing cross-account roles here and reiterating, whatever you can do inside your AWS account, you can do with cross-account roles except for a handful of actions. That's my 2 cents would be just to use cross-account roles.