I haven't completed it yet but this is from multiple instances within his book God's Playground: Volume 1 on the history of Poland. From what I know of Polish government from other sources on the topic, it was somewhere between an oligarchy and a parliamentary monarchy. Do the Sejm, Szlachta, etc. create a system which fits the definition of a republic?
Truth of the matter is, that Polish nobility consisted of 9% of the total populace. That meant that effectively, Poland would have been a democracy on par with many states that later thought themselves as democracies or republics. The other thing was that an oligarch and a poor nobleman were equal in rights legally speaking "na zagrodzie równy wojewodzie etc."
The name of the country itself was "Rzeczpospolita" which is a polish translation of the word republic, though the sovereign was technically the king.
I think that because it was as much as 9%, the king was elected, and the nobility were equal in rights - I'd venture to say that Poland was, in fact, a republic.