It's a bit of a mix - it's not as bad as the reports say but they're definitely around. I have lived around Auckland most of my life and the most common cockroaches you might find around the home are ~1cm long. Because the standards of most buildings (especially if you rent) aren't great, it gives bugs more of an opportunity to get in to the house. Also the closer you are to forest or bush the more likely that you'll have visitors.
So, I can't say you won't see them, but they're not that big and I haven't seen any that fly.