Assuming that there's some small but non-zero chance of a randomly selected line intersecting with a star in a finite volume of space, it's pretty clear that for an infinite volume, the probability of hitting at least one star will approach 1. (So long as the density of stars is approximately constant, or at least has some lower bound.)

And since stars are not point like objects, a line does indeed have a non-infinitesimal chance of intersecting a star.

Although all of this is a bit different from arguing about the net brightness of light coming from distant stars.