We don't know enough about the characters and the houses from that era.
We know the major relevant houses and most of the kings, and CKII can fill in the gaps automatically. Here, here's the major characters we know of:
Principality of Dragonstone
Aegon Targaryen, Prince of Dragonstone
Visenya Targaryen (older sister, wife to Aegon)
Rhaenys Targaryen (younger sister, wife to Aegon)
Orys Baratheon (bastard half-brother to Aegon)
Kingdom of the Iron Islands
Harren Hoare, called the Black, King of the Iron Islands and the Riverlands
Edmyn Tully, Lord of Riverrun, vassal to Harren
Victarion Greyjoy, Lord of Pyke, vassal to Harren
Kingdom of the Stormlands
Argilac, called the Arrogant, King of the Stormlands
Daughter of Argilac, Princess of the Stormlands (name unknown)
Kingdom of the Rock
Loren Lannister, King of the Rock
Kingdom of the Reach
Mern IX Gardener, King of the Reach
Harlen Tyrell, Steward of Highgarden (Master of Coin of the Reach?), courtier to Mern
Unknown Hightower, Lord of the Hightower, vassal to Mern
Kingdom of the North
Torrhen Stark, King in the North
The Night's Watch
Unknown Hoare, Lord Commander of the Night's Watch, brother to Harren
These are just the characters that are specifically mentioned. A number of other houses (for example, Arryn, Martell, and Bolton) are known to have held their current titles since before the Conquest. The biggest problem I see is that the Storm Kings don't seem to have a house name. We also don't know the specific first names of a bunch of characters, so we might have to make those up. Either way, though, CKII's engine should automatically fill in any gaps with appropriate randomly generated characters,
a la Rome (I think it may even do this with partially defined characters, so that in theory we could still use this mechanic and define nothing more than house names)