Being immersed with no alternatives does force one to learn simple phrases to get by but it seems quite possible that you'll never have non-trivial conversations with locals until you have enough vocabulary -- and locals won't have non-trivial conversations with you unless you have enough vocabulary. Also native speakers are often loathe to correct you when you make mistakes, so the feedback loops is often broken. To get out of this chicken and egg situation, it seems to me that some amount of focused study is required, and whether that is done in the country or outside doesn't seem to matter (especially with sites like iTalki or others).
As an example: I have friends who taught English in Korea for years (where English isn't widely spoken). They were able to function for years with a few choice phrases and never needed to go beyond that.
Sometimes even at significant levels of immersion, it's possible to not be able to speak the language beyond the basics. I have friends who attended German universities, in German, but have trouble speaking German. Likewise in the US there are many international students attending college in English, do fairly well in school, but struggle greatly to converse in the language.
I think immersion is merely a tool: the underlying driving force really is "intention". With intention, it's possible to go much farther even if immersion was not a tool at one's disposal.
Another nice thing about immersion is that you can engage with cultural events that may not be present in your own country, and gain a deeper understanding of the natives themselves, which ties straight back into the language.
Depending on the country or your living situation it can be really hard to branch out... learning while living in a student dormitory was great because I was forced to express myself, even if I was sick, felt less motivated, missed home, etc.
Immersion works when there's no other way around it. In particular for native english speakers, you'd have to be in a situation where either most people you interact with don't know enough english for communication to be effective, or (and this is very rare in my limited experience) you would have to make an effort to stop using your native language altogether, even when locals address you in it. It also helps when there aren't any family/friends/compatriots around so you can't really "cheat" and you won't be able to function on a daily basis unless you learn and practice the local language.