The existing evidence overwhelming suggests that a computer that can "learn to produce infinite, novel, contextual, and meaningful grammatical utterances" will be based on probabilistic models. In fact it's hard to imagine how it could possibly be otherwise.
The computer is observing noisy sensory input and is trying to make inferences about how to communicate with some future reader. Mathematically, there is only one way to write this problem: probability. It's true that the learned model may have amazing structure to it, but this will almost certainly be learned via probabilistic models rather than being hand-coded by some future Chomsky.
That fact does not imply we will understand language systems or the human mind. The Chomsky route may be better suited for that task.