Can I learn to speak English by just living in an English speaking country without taking any courses?

Yes, you can learn English just by living in and English speaking country but only with a great deal of determination. This is essentially how I learned Chinese. I landed in China with a job teaching English – I never had any Chinese language lessons, I just interacted with the local people and gradually picked up bits of the language. Things accelerated when I married a Chinese woman and started a family – as I was pushed to expand the scope of my language into new areas. The downside is that you tend to learn only small subsets of the language that relate to your day-to-day life e.g. shopping, cooking, dating and work. You miss out on some of the less common, beyond your personal experience, subjects. This means that you may, after some time, find yourself doing a new task – maybe starting a new job – and don't have any of the words need to accomplish the task. To keep learning, you have to keep pushing yourself into new situations, thus encountering more new language. A course or a book will naturally cover a broad range of topics, constantly pushing you to learn new things rather than simply become more fluent in the things you already can do.