Very old video here, but I last tested this right after we got the Unity port on PC and you could still hit through entangle with Bullseye. Same with Assassinate, and Voracious. Zero attack/zero damage dealt don’t matter at all, the only condition required for it to proc is matching skulls while in the first slot. Barrier will block a single otherwise lethal hit from Assassinate or Bullseye (not sure about Voracious, it takes way too long to get it to trigger to repeat the test conditions)
Status application traits do however require damage to be dealt with skulls (if you absorb the hit with a barrier or dodge with Agile trait, no status is applied, either). Psion only cares if its Attack is > 0 when it matches skulls in the front position (be it via entangle or straight reduction) - if it is, it will steal mana regardless if the attack hits a barrier or is dodged with a trait. Because of this, Psion is the only skull trait that is completely shut down by entangle, because every other one can just get a match 4/5 to trigger it (or will just trigger regardless).
Consistency would be nice, but they are obviously coded differently because of how they do different things. I do think it could be clearer how they work, though.