In a manner of speaking, yeah.

I'll preface this by saying that the countries of the Eastern Bloc cannot be classified as some huge totalitarian monolith - different governments (even different governments in the same country) enacted different policies and supported differing things. Likewise, the citizens of different countries had different cultural backgrounds, outlooks, motivations, etc. It's impossible to talk about the Eastern Bloc as a whole. Behaviour and policy in Poland differed from behaviour and policy in Romania, which differed from behaviour and policy in the USSR... you get the idea.

When we talk about counter-culture, we think of culture that is anti-establishment: opposed to social norms. What does this mean in the context of the USSR and the Eastern Bloc? The adoption or appropriation of Western culture? Or does it need to be culture that is actively anti-establishment or anti-authority?

As for the former - adoption of Western culture - that is something the Communist authorities did have to deal with. Modern Western fashion, hairstyles, and music were popular across the Soviet Bloc. Wearing blue jeans, listening to rock and roll (for example) was counter-cultural in the sense that it went against official ideas of how a good communist citizen should dress and act, but it wasn't necessarily a focus of anti-establishment activity. Communist citizens could listen to the Beatles, or wear a pair of jeans, or grow their hair long without necessarily thinking of themselves as being bad Communists - despite knowing that the state condemned Western culture. Alexei Yurchak has done some really interesting work on this 'paradox' in late Soviet culture - his book, Everything Was Forever Until It Was No More focuses on the last generation of Soviet citizens in the USSR from the 1960s - 80s. It's a really interesting read.

While not everybody who appreciated or adopted certain aspects of Western culture held anti-establishment views or ideas, cultural groups which became focal-points of anti-establishment activity did exist, and Western culture sometimes was a starting point for them.

The musical underground is a good example of this. It wasn't necessarily always extensive, but it was persistent, and was a vehicle through which people could become introduced to anti-establishment views and ideas, despite not being a 'proper' opposition itself. Sometimes indigenous bands formed loci of opposition; sometimes Western artists inspired anti-establishment activity. John Lennon's death, for example, was important in uniting people who held anti-establishment views - the Lennon Wall in Prague is a remaining monument of the John Lennon cult that existed there prior to the fall of Communism. If you'd like to read more widely about the music underground across the USSR and Eastern Bloc, I'd recommend Rocking the State, a collection of essays edited by Sabrina Petra Ramet, as a good starting point. Padraic Kenny's A Carnival of Revolution also discusses how the countercultural movements of younger generations impacted the fall of the communist systems in certain parts of the Eastern Bloc.