Does Doomsday Dawn contain spoilers for Iron Gods?

My group is about to start playing Iron Gods, with me as the GM (My first time doing so). One of my players wanted to run the playtest adventure on the side with just a couple of us. Last night, he texted me that he thinks there are Iron Gods spoilers in Doomsday Dawn and asked me if the Dominion of the Black is important to the Iron Gods story line. Apparently he knows about how the starship crashed in Numeria, but he says he hasn't read past the intro.
Are there any other spoilers for Iron Gods - particularly for book 4 - in Doomsday Dawn? Should I let my player run the playtest adventure?

From what I can tell Doomsday Dawn does not contain spoilers for any other adventure path. Every chapter gives a brief introduction where it fits in the timeline and which adventure path is happening "in the background", but it does not say anything about the story of that adventure path.
But yes, the Dominion of the Black is very important for Doomsday Dawn's story.