Actually, up until Rough Beasts of Empire, we had no idea by which members of the Romulan Senate were selected. Rough Beasts established that the Senate is comprised of representatives from the Romulan aristocracy, the Hundred families, whose clans appoint one of their own as Senator.
Meanwhile, both the novels and the canon have established the existence of a Romulan monarchy. The Emperor or Empress usually ruled as a ceremonial head of state, with the Praetor as the head of government with real power. The Romulan throne has fallen vacant since the assassination of Shiarkeik, but there's been no indication that the Monarchy has been formally abolished.
So, no, the Romulan Star Empire is neither a democracy nor a republic.
One problem is that Pardek is stated in "Unification" as representing the Krocton Segment
, a territory on Romulus. He's described as a "man of the people" who carries on a successful dialogue with the residents of the Krocton Segment.
At the very least, there were seats representing territories in the old Senate, before it was restored by Tal'Aura.