Definitely going places where English is spoked have helped but it would have been possible without. We didn't spend enough time on each visit to make a huge difference but it helped psychologically. They often made slight improvements after each time but our language success was not solely dependent on those visits.
My children would still be fluent in English, even if we hadn't made so many trips, because that's the only language we use on a daily basis together. I personally know quite a few families where the child is fluent in only one parents' language.
Remember too, we are talking about the ability to speak the language. The example you gave of a Croatian child, perhaps growing up in N. America, would be a good example. They still can be fluent, if the Croatian speaking parent is consistent and tries to expose the child to the language through other mediums (books, DVD's, Skype, etc.)
The new technologies are really making this task so much easier! No more hunting down English language cassettes (just switch the DVD) and communication with friends and family is so much better than just 10 years ago.
If you took that child and placed him directly in a Croatian language school in Croatia, probably he would not be able to pick up the material right away nor would test at age level. I know mine would have difficulty if we suddenly moved to the States.
Most international parents at least make a few visits, if not, family come to visit them (especially in say, a refugee situation). Where I'm from, there are a lot of people originally from Iran. Their children still speak Farsi, even with only one parent from there but visits to that country are out of the question. So it's actually rare to have a child completely isolated from the culture and people of that language (although I'm sure it exists, I don't know any cases like that).
So success, if you measure it by the fact the child speaks the language, is possible. You may not have a completely, equally bilingual child as you would if you, for example, lived in Southern California or Texas and spoke Spanish. My kids don't have the level of vocabulary or the writing ability of American children their age. They also make mistakes children their ages wouldn't, but they speak English with an American accent. New words and writing ability are something that can be worked on later on.
The advantage children have when little is to learn to speak another language without an accent, without relying on their stronger language to communicate. I may have to listen to a whole minute of "the thing that you use to...that looks like..." because she doesn't know what an egg timer is called in English but she's explaining it without an accent in English.