According to this and what I read above and from having one myself I don’t think you do since they are both incorporated into the tag with a lot more then we know attached to it as well.
That being said even tho I have the tag I’ve left it running in my home background playlist just cause I forgot about it being there till I saw this post lol. But I don’t think it’s necessary according to what I’m reading.
And the tag can be pretty intense to wear anyways so maybe just stick to the tag and one less audio for you to have to worry about on your environmental playlist.
Good luck and fun to you on the bouncing gig man @PatronSaintBiceps