Yes.
Time period-wise, I was thinking shortly before Renly's death. That would give us five Kingdoms (House Greyjoy and King Balon Greyjoy, House Lannister and King Joffrey Baratheon, House Tyrell and King Renly Baratheon, King Stannis Baratheon, and Houses Stark and Tully and King Robb Stark) as well as the neutral Houses Arryn and Martell. Of course, some Houses such as Florent, Hightower and Frey would also be playable despite not being of the Eight Houses (Greyjoy, Stark, Arryn, Lannister, Tully, Tyrell, Martell and Baratheon), as they are fairly strong as well. As Queen Daenerys Targaryen and her army still have not affected Westeros by the end of A Storm of Swords, I think she can be left out.
Of course, whoever is playing Renly Baratheon would probably not want to be so stupid as to go to Storm's End himself... (In other words, the NES will work best if all players have some basic knowledge of the books.)