Welcome to Microsoft Q&A Platform, thanks for posting your query here.
The installation of the ASDK on an Azure VM is not supported. Please refer this ASDK requirements and considerations documentation.
As far as what a global admin can do on a subscription, that is also well documented, and while the installation itself is not going to necessarily cause an issue, anyone that has access to that account would be able to make changes to the broader environment.
The global admin is necessary to register the the Azure Stack object to a subscription - I'm not aware of anything from a tenant perspective that gets altered.
Hope that helps.
Please 'Accept as answer' if the provided information is helpful, so that it can help others in the community looking for help on similar topics.