User blog comment:Darkcloud1111/''The Mark of Athena'' Plot Holes/@comment-3146930-20121014230006/@comment-3146930-20121014231322

Nope, Nico even says that Thanatos wouldn't go down there:

"Even the gods don’t go into Tartarus. Even the god of death, Thanatos himself, wouldn’t go near that place."

And even if Tartarus has different levels, Percy, Grover, and Annabeth were almost pulled in during The Lightning Thief and they were just at the edge. As far as the questing part, Nico found the locations of the Doors of Death, but he wasn't on a quest, at least not officially. I guess you could say that the 7 were on a quest to save Nico, resulting in them finding out the location of the Doors of Death, but that is kind of cheating in my opinion.