A family of Microsoft word processing software products for creating web, email, and print documents.
Yes, you can rename normal.dotm and use it as a Global Template.
It will be rather large though.
Which customizations are you trying to share? You can easily share the following in a global template:
macros
keyboard shortcuts
QAT modifications
Styles are usually best shared via document templates but can be shared through a global template using VBA:
A Global StyleSheet in Microsoft Word?
Any template becomes a global template when placed in a user's Word Startup Folder .