I won't quote any serious research, but in my experience, adult persons completely reliant in induction techniques don't learn new languages effectively.
I had a girlfriend many years ago studying English by means of using the Callan Method, she didn't learn much except a few random words. I know another person who moved to the UK and has been trying the same method, her English is horrifying.
And I got four work mates who use this duolingo app; one uses it to learn Italian because he is married to an Italian lady, the other tries to learn Spanish just because he likes it and the other two are trying to learn Japanese. Now, I speak Portuguese, so I can understand and communicate with Spanish speakers and Galician speakers, and I also speak Italian. I spent years studying Italian, and I don't consider myself fluent, but I understand it really well and I am quite sure these gentlemen can't speak their respective chosen languages. I don't mean they are not fluent, for they certainly are not, but they are utterly unable to formulate the most simple sentences. The bloke who wants to learn Italian can convey some ideas by using isolated words and often mix them up and doesn't pronounce them very well, but he doesn't know anything about how to construct a sentence, use different grammatical tenses, connect words phonetically, etc. The one trying to speak Spanish tried with a Spanish colleague of ours, he couldn't speak more than a dozen words without giving up.
I guess the bottom-line is: adults don't learn like children do. Children have no interaction with sophisticated language systems before they learn their first languages, therefore it is easier to them to listen and repeat and use it often, because they have no shortcuts, that's all they have to communicate. Also, children have adults all the time pointing out the names of things, correcting their grammar and pronunciation and constantly providing them new vocabulary. When a child errs, it is only natural; but when an adult errs, it could be a source of embarrassment. Of course some people don't care and that's the correct attitude, but I do think adults tend to be more cautious and they give priority to master the speech before putting it to use. It means they don't try as hard a a child.
Also, children are surrounded by an environment using a specific set of languages. An adult can only put himself in that situation my migrating to a place where that language is used. You won't learn Italian properly in the UK unless you lock yourself in a place where everyone uses Italian for pretty much everything.
So I think induction doesn't work. It is the same as memorising random words. If you don't use them they will be forgotten soon enough. Learning grammar is the best route, because this way you learn the structure of the language. Later on, by learning vocabulary you understand what that word represents and how it can be put to use. As long as you apply the same rules constantly and practise, it becomes a subconscious exercise and you eventually stop thinking about that because you get fluency. By getting fluency you gain access to more content (books, telly, radio, conversations, etc) and you gain even more fluency.
That's my experience, I'm sorry I am not citing any researches. Or rather, that's my personal research into the matter; the population in this research is very small, perhaps there are others more thorough. =D