I found I made deep friendships more easily after speaking even a bit of Russian. If you can say "My name is X" and "awesome" and a couple other small phrases it helps. That said, it wasn't until I had put in around 1000 hours of practice until things really opened up. It's such a hard language and I'm below average in my ability to learn human languages. But I did make steady progress with Verbling and I even met up with my tutor when I was in Ukraine.
One of the things that learning Russian clears up is why they sound so angry to English ears. The language doesn't use tone for emphasis as much as English. It uses word order because the grammar is more flexible so they're able to put the important stuff at the end. Plus the sounds are more constant based. So once your ears get used to the language, you don't really hear Russian (or a Russian accented English) the same anymore. It sounds more human. Plus you learn so many words, you end up finding some of the endearing / superior to the English translation.