Omg I just found this on the Official site and it definitely states that the greeks and Romans will fight

"Told from the perspectives of four different demigods, including Annabeth from Percy Jackson and the Olympians, The Mark of Athena unites the Greek and Roman main characters from The Lost Hero andThe Son of Neptune.

In a fantastical ship called the Argo II, seven demigods journey by air across the United States and by sea to Rome on their quest to defeat the earth mother, Gaea. Meanwhile, war is breaking out between the Roman and Greek demigods they left behind, and only Annabeth holds the key to restoring peace."

yes check that out that tells that they will fight.

Any 1 else is free to post any more new info on this topic!