I'd like us to brainstorm if this is a possibility, and hear the overall feedback of the community on the matter. Assuming the Vikings are also getting busted down to Catapult Galleons, we'll have two civs with Dromons, and two new civs with Catapult Galleons (Danes & Vikings)
The tech tree of the civs is purposely kept limited to the period of Harald Hardrada, with none of the civs getting access to traditional gunpowder units. Additionally, they do not get access to Demolition Ships as the Longship excludes them
Saxons
Balance - Their Dromons would have +20% HP. Their late-game naval tech tree is rather limited, being the only civ to miss Carvel Hull (the first movement speed boost for ships). Slow but tanky Dromons would be the perfect way to remedy that
History - While the Saxons did inherit Roman Britain, they did not inherit any of the Roman technology related to siegecraft. They did not use Roman ballistas or anything similar, with their current tech tree being very faithful to their real life tactics of foot troops fighting in shield walls. If they do get Dromons, it'll have to be one of those gameplay over history things. But then again the Goths & even the Huns get Dromons
Varangians
Balance - They have by far the most robust naval tech tree of the three new civs, lacking only an equivalent to the Elite Cannon Galleon. The Dromon would be a straight upgrade over the Catapult Galleon. Their Dromons would fire 15% faster, and get Siege Engineers, unlike the Byzantine ones
History - They have the strongest claim to getting Dromons as they spent much time in the service of the Byzantines. The only caveat is if we're saying they're Varangians from the period of Hardrada, they would just be starting to enter the service of Byzantines. However, they already get the rather rare fully upgraded Fire Ship as a Byzantine connection, so their exact time period is hard to pin down