The discrete approximation to the integral involves sampling the function at a finite number of points and then computing a weighted sum of the sampled function values. In the case where N = 2, θ only takes the values 0 and π and the approximation is f'(x₀) ≈ 1/2 * (f(x₀+1) - f(x₀-1)), i.e. approximating the derivative with a simple difference.

So I don't think this is more biologically plausible than neurons using finite differences to do gradient descent.