Nope. They wouldn't not bet treated as Austrians. The Empire was very hierarchical. And the order was:
Note that Czechs are 3rd. Franz Kafka was 6th.. which is why his writings are so frustrated! Now you already understand Kafka better...
It absolutely mattered. But Czechs (who were highest among the Slavs because they had the most industrial part of the Austro-Hungarian Empire... so I'll just compare Austrians with Czechs.. but Hungarians were in-between) mattered more and more as time went on. They started to get more rights, like learning Czech in school. Austrians wrote about their worries of the ever-increasing power of the Czechs. But this power was actually very small.
And then to complicate things, German speakers with Czech names, and vice versa were extremely common.. so it's not like the lines were thick and solid. Rather the ethnicities mingled quite a bit! (and can still be seen in places like Austria, the Czech Republic and Slovakia)
Anyway, we talk about this ALL THE TIME on the bohemican podcast ..it's what it's all about. The parts that aren't mentioned on Bohemican, will eventually get covered on the History of Germany Podcast's (http://historyofgermanypodcast.com) History of Austria mini series (on the Hapsburgs, and the Empire, etc.)