Poking this phrase apart, this is what I get out of it:
1) It does not say, "The creature can make a grapple check to do the damage..." ... it says "Each successful grapple check it makes ... automatically deals the damage ... ". This seems to mean that as long as you're rolling an opposed grapple check, you can do damage, be it with a pin, an escape, or an attack. I can visualize this; the snake has its fangs in the person, and using grapple checks to hurt the opponents is just pushing the opponent around. The snake is swinging the person around with his fangs stuck in him. Poor guy. Likewise, when the snake tries to flee a grapple (yeah, right), he flings the guy off the fangs. That's got to hurt. But flavor text aside, it seems that the damage is dealt.