Yes. But the problem is people have a very hard time doing that. You cannot engage with EU level politics the same way you can in a real country. All these people speak different languages. Very hard to stay engaged when you have to listen to translations. You hardly ever get the kind of engaging coverage you would for domestic politics.
I know most of the politicians and parties in my country. I would easily recognize and have some opinion about most prominent congresspeople and senators in the US. Same goes for knesset members. Yet off top of my head I couldn't name you 10 EU MEPs. I know names of the biggest parties in the EU parliament but I couldn't tell you much about them.
Unless EU actually tries to establish a common culture and a common language, I don't see much changing.