I think this question needs more definition. When it's asked, "Can people become more intelligent in response to environment," my first reaction is to say, "Absolutely! If the environment demands more intelligence, it will develop. See Darwin."
I wonder, though, whether the intended question was "Can *a person* become more intelligent . . ." The question has a little more breadth taken this way, and requires a fine definition of "intelligence."
Wikipedia.Org says this: "Intelligence is a property of the mind that encompasses many related abilities, such as the capacities to reason, to plan, to solve problems, to think abstractly, to comprehend ideas, to use language, and to learn."
I think it's fairly to say that the components mentioned in that definition are improvable - we all improve on them throughout our lives, to some degree.
(This seems to miss the main sweep of the question though, which is really flirting with nature versus nurture.)