Yes, that will break Zotero Word integration completely.

I don't know all the details, but Word provides various ways to restrict macros to specific locations, files, and publishers. Since Zotero.dotm is signed by us, it may be possible to configure things on all university-owned computers to trust its specific publisher. (You can definitely do it on-demand on a single computer, but I'm not sure what would be involved in doing it more broadly.)

https://support.office.com/en-us/article/add-remove-or-view-a-trusted-publisher-87b3d5a3-b68c-4023-87c4-7cc78a44d7ed