uMatrix is awesome as it disables any 3rd party domains and only loads content from main domain that author controls. it also allows blocking by content type. Like iframes.
I believe some blockers designed for telemetry blocking, like ghostery or privacy badger, will come with js shims. So they will block google tag manager, but will load a replacement JS to make sure the page doesn't behave in a broken way.
uMatrix is more general purpose and does't do shims. Saying this, website should detect telemetry didn't load, and either still work, or display error saying why it can't proceed.