Given the fact that we can build a computer in the game of life, this breaks down to a simpler question: can we have intelligence in a computer? If so, it can also occur in the game of life.
It would be difficult. In particular, unlike in our world, it's very difficult to create anything like a stable membrane or barrier in the game of life. And patterns are extremely susceptible to falling apart if perturbed. So you would generally expect a game-of-life-based entity touching anything to die as a result.
Since the game of life is Turing complete, it can simulate any computer. If a computer can eventually simulate the world (including humans), so can the game of life.
This doesn't mean the patterns would visually look like cells and membranes though...
Turing machines in the game of life have the same problem of being unprotected and extremely sensitive to perturbations. It drastically lowers the chance of generating a working one (even when running for extremely long times on extremely large boards). Contrast with our world, where it seems like just starting with a whole lot of randomly distributed hydrogen could be enough.
It's hard to imagine an emulated version of a human having a consciousness, however. What is it that separates transistors firing randomy from a CPU executing specific consciousness-generating instructions? I find these things thought-provoking.