No, as long as both organisations have the same contact email addresses for the profile owner. If you use different contact email addresses for schools, sports clubs, Scouts etc, you will have to create a care profile for each of those email addresses, or alternatively change the email addresses for a care profile to the same email address. The care profile you have created for yourself or your child can be shared multiple times. This means you only need to update one care profile and the group, club, school and individuals you share it with have access to the same details. When you make an update all carers who can access the data have the latest information.
The invitation to create or share a profile with Scouts NSW will provide links both for creation (for new users) and to share (for existing users). Click on the relevant link and follow the prompts. Refer to How do I sign up?