No sir, there was a mix. Any time you see a Lithuanian surname with "-auskas" it's because of exposure to Polish culture. There were tons of Poles in Vilnius. And Lithuanian aristocracy became rulers of Poland, starting with Jogaila.
But the most ridiculous thing is that multiculturalism killed it. It was partitioned by foreign imperial powers, eg. split between Russia and Germanic powers.
I would also argue that Poland being culturally dominant in the union, and eventually translating it to political dominance (of e.g. Roman Catholics over Eastern Orthodox) severely diminished the original GDL multiculturalism, which was much more pluricentric and religiously tolerant.
And that, arguably, was one of the causes of its eventual demise - e.g. would Ukraine have rebelled if they didn't perceive themselves as second-class citizens in Rzeczpospolita? And if it didn't, would Russia be able to eventually take over half of Poland?
But the most ridiculous thing is that multiculturalism killed it. It was partitioned by foreign imperial powers, eg. split between Russia and Germanic powers.