Look up the Safir-Whorf hypothesis for some interesting discussion about this kind of thing. Most psycholinguists and acquisitionists tend to conclude that it’s extremely unlikely that a person’s language fundamentally effects the way they percieve the world, but it’s also extremely hard to prove things one way or another.
Also, just as a technical quibble (so feel free to ignore this paragraph), learning a second or third language to complete fluency after the age of 5-7 isn’t going to make you a “true” bilingual, since primary and secondary language acquisition are very likely completely different processes when you get down to the neural circuitry involved.
An easy way to argue this is to look at the manner in which people learn natural languages. Basically, while learning a language (and, for our present purposes, I’m going to claim that learning a language simply involves learning its grammars: syntax, semantics, phonology, the whole deal) while completely immersed in it (as is the case with infants), there are two possible types of evidence that can be presented to you: positive evidence, which provides information about what is grammatical, and negative evidence, which provides information about what is not grammatical.
Now that you’re armed with these two definitions, it’s easy to claim that adults and children learn differently. So here’s what I would propose: first off, I think most of us can agree that all newborns start with the same information about the grammar: some people claim kids start with nothing, others claim they start with a heavily coded input layer that allows felicitous structure to be processed sequentially, and a lot of people claim that they simply restrict the possible set of starting structures. That last idea ultimately ties into Universal Grammar, or UG. But none of that really matters: for our purposes, let’s just say that all kids start with the same roadmap, which we’ll call the initial state, or S(0). Hopefully they’ll eventually end up in the final state, s(n), at which point they should be roughly homogenous with their speech community. Now, obviously this isn’t 100% accurate: dialectal differences, register contrasts, and a whole host of individual variation is to be expected. Really, it’s something that always amazes me: given the sheer breadth and depth of variation we see in human speech, people still manage to identify and catalogue systematic modulation well enough to create a homogenous speech community. (On a tangent, think about what would happen if you were to drive from village to village from, let’s say, the center of France to the center of Italy. I can almost guarantee that every village will be comprised of a homogenous speech community, and yet the villages just to each side of the border will be much better at communicating with each other than two villages pulled from the far corners of each country. And that’s just cool.)
But anyway, you see what I’m getting at: it’s logical to expect that newborns should all start with the same lingual capacity, namely the initial state, and that all children who’ve grown up in the same speech community should end up with the same final state. How can we prove this? We can prove it by looking at grammatical intuition. If you’re a native English speaker, you should (hopefully!) have an inate sense of what is and isn’t felicitous in English. If I say “Dog ran the” and “The dog ran,” most native speakers will instantly know that the former is ungrammatical, and the latter grammatical. Note that I’m not talking about the grammar you learned in school here: that’s prescriptive, and it’s purely intellectual. What I’m talking about is what a well-schooled grammarian and someone who has never taken an english course in their life both understand in the same capacity, assuming they’re both native speakers. And of course there exists regional variation in grammar, but anyone who has grown up with a certain dialect should ideally display homogenous intuition.
So we’re looking at how all babies get from the same start point to the same end point. And in the name of being brief, they do so with what’s called Text Learning: essentially, they do it without any negative evidence whatsoever. (You can test this on your own with a 1.5-2 year old, if you’re feeling extremely patient.)
Adults, on the other hand, are the exact opposite: they absolutely thrive on negative evidence, and are substantially better than children at what’s called Informant Learning, which is a process of acquisition based entirely on negative evidence.
Now, logically you would assume that negative evidence is essential for anyone, since with an infinite number of possible utterances (which there always are; languages are always infinte and recursive), we would predict that children, deprived of any negative evidence, would frequently produce novel forms that fall outside the bounds of the (extremely limited!) parameters that a given language finds grammatical. A very well-known theorem to this effect reads “Only languages of finite cardinality are text learnable”.
So if this is true, why is it that infants, as text learners, can go from an initial state to a quasi-homogenous final state soley on the basis of positive evidence?
Universal grammar! I’m not convinced UG in its present state is anything close to what actually happens in the brain, but it’s a really great theory speaking from a mathematical point of view.
So anyway, if anyone’s actually still reading I hope the meandering talk about adult versus child acquistion drove home the on real thing I had to say, which is this: despite surface similarities, the manner in which adults and children learn languages are almost polar opposites. Since they aren’t identical, we can’t possibly expect adult learners of a language to exhibit the same neurolinguistic tendancies that children do. 
I tried to keep this brief… if anyone wants me to elaborate on something, feel free to ask!