No, this tag is about helping people homebrew their own content.
Firstly, let us look at the current guidance offered by the homebrew tag description:
For questions about homebrewing new rules content for an existing system, this tag should be used when locally-created, non-published content is at the heart of the question.
and
This tag is for questions about creating new rules material
This tag is supposed to be used on questions whose core focus is on actually developing homebrew. That means helping people to develop new content. As it is written now, its purpose is not to mark questions whose content comes from non-official sources.
Generally, tags are for categorizing the core focus of the content of a question, not what book or URL that content happened to have originated from.
Not only that, but marking such questions with this tag also goes against the tag guidance in another way since it says it is explicitly for
when locally-created, non-published content is at the heart of the
question.
Blood Hunter is published 3rd party content. It is published on DnDBeyond and it is even published on DM'sGuild. Thus, it does not qualify as homebrew-related for our tagging system.
Is the DMsGuild considered Homebrew and if so, should we always use the homebrew tag in parallel? also came to the same conclusion with DM'sGuild material in general.
So, unless a question is about developing homebrewing content around or with this content, the homebrew tag is not appropriate.
We could create a new tag for Critical Role content
(as suggested by @Oblivious Sage)
I'm not sure if it is necessary, but since people keep trying to tag Critical Role material with something I think it might be worthwhile to create critical-role to be a tag that can fill that role.
As @doppelgreener points out, we have a standing policy of tagging 3rd party publishers so this would fit that as well.
Regardless of whether or not a tag is created, though, homebrew is not appropriate to use for questions about Critical Role content.