I think Fulgrims fall to chaos was more due to the daemon with the sword of the Laer wasn't it? From memory, Fulgrim didnt get blade until he came to Horus on orders from Terra to check on his methods of Warfare. By this stage, the whisperings of the Laer sword daemon had become his second advisor in his head.
At least I think thats how it went
You are correct. The Sword of teh Laer was possessed by a Slaanesh daemon. The Anathema is present in the Fulgrim book, but Fulgrim only wears it around Horus. Later he doesn't even do that...
((Spoilers about HH: Fulgrim))
Thought one would argue that Fulgrim never fell to Chaos, but his flesh was possessed by the daemon. Remember the horrible portrait that was painted of Fulgrim? As the story progress the portrait changes and becomes Fulgrim intact with the Daemon possessing him. In the end the daemon even claims it trapped Fulgrims mind inside his own body because the Daemon enjoyed how he screams and cries as the Daemon use his body to swathe through the Loyalist Space Marines. And specially as the Daemon killed The Silver Handed Primarch.