First off, yes to the part about photons (as waves) traveling indefinitely until absorbed. However, no to the second part — a photon will never reach the “edge of space” for two reasons. First, space itself expands faster than light speed. And second, since space expanded everywhere at once and is isotropic, any random photon has (today) 46B light years of its own observable event horizon in all directions, and there’s plenty of matter filling that space just as within our own observable universe. Whether our own galaxy is within that photon’s event horizon or not.