I did some testing on this this morning:
They seem to take 350 damage before they explode.
There is no chest or headshot multiplier.
They start tracking at around 3 meters but will keep tracking until you are about 6-7 meters away. Obstacles don't affect this.
There is no team damage.
They will not take damage/explode if they aren't in the process of tracking you.
Shields/Cover does not prevent you from dying, neither does EOD.
Overall nice easter egg. Wish they would react to emotes or something, that would've been funny.
Edit: typo. It's 350 damage, or about 4 weapon melees.