I think this is true. Although I don't have a formal proof. I haven't read the original Denavit–Hartenberg paper, but this paper: "Lipkin 2005: A Note on Denavit-Hartenberg Notation in Robotics" explains the 3 main DH parameter conventions and how they differ. It breaks down each of the 4 parameters into vector forms. Specifically:
$$
a_2 = \vec{{O}_1 {O}_2} \cdot {x}_2
$$
Where $\vec{{O}_1 {O}_2}$ is the vector between the two frames. The dot product can be negative, but only if the angle is greater than 90 degrees. But because of the strict way you construct the frames, I don't think that can happen.