Interesting question.

The purpose of an IQ test, I believe, is to identify individual variation in cognitive processes. These tests do this by asking individuals to engage in mental tasks that could be performed by some individuals, but not others. Thus it seems logical that an IQ test would define mental tasks that could not be performed by individuals with an IQ below a certain point.

The question you have, though, is whether or not these mental tasks are completely inaccessible to some people, or if everyone can complete these tasks given the right circumstances (more time, or perhaps more education or life experience, or whatever). Does this sound right?

Personally, I'm not sure of the answer, but it is something that I contemplate. My personal anecdote that informs my thoughts on this is that when I was a young teen I had very strong cognitive abilities, but during my later teens I suffered from frequent undiagnosed seizures which affected some (but not all) of my cognitive skills. I have now been treated and my cognitive skills appear to be similar to what they had been originally. One could argue that I suffered a temporary drop in IQ. It is my personal experience that (particularly because of my decrease in short term memory) there was a point that, no matter how hard and long I tried, I would plateau and not be able to go any further in some tasks. I mean, yes, there is a chance that if I tried hard enough and long enough, I could have done as much as I expected myself to. But practically speaking, it was hard and wasn't worth the effort.

Once my cognitive skills increased again, it was like life was on "easy" mode. I don't have to work half as hard as I did before I got treatment. The way I see it, people with lower IQs are probably capable (unless they never developed certain cognitive abilities at all to begin with), but are completing mental tasks on "hard" mode. (Or "medium," I guess, if they're average).

So yes, I would guess that it's possible for just about anybody with a "normal" IQ to perform the mental tasks that a high IQ person could perform. I suspect, though, that it would be impractical for the "normal" person to do so, as it would not be worth the time and effort that it would take.