Hello bob8. Welcome to the Kitz forum.
You ask a very good question and, to be honest, my answer is to say "I do not know". It would be best to assume that the busy-body has more than one method of "calling home" so even with the tagged vlan deleted, it would also be prudent to terminate the BTAgent. (The super-cautious will also unmount (using a umount call) the partition that is provided for its activity.)
A BTAgent can be found in the firmware of other CPEs that bears the Beattie Group name, so I would assume that there is a significant degree of commonality between all the variants of the little snitch.