Bruce is right on the 1g acceleration- from the ship's point of view. As the ship gets nearer the speed of light, to an Earth- bound observer, it seems to almost cease to accelerate as it asymptotes to c. But from its own point of view, it keeps on accelerating.

There are still big problems- although they can travel 60 or 70 thousand light years in a few generations, by the time they got back here, 120000- 160000 years will have passed on Earth, which is as long as modern humans have existed. Goodness knows what kind of reception they'd get. Even assuming they didn't bang into anything on the way, and 5 or 6 generations down the line, they've remembered what they set off for. Just navigating back to Earth will be hard enough, as it will have moved.

Perhaps the Neanderthals developed an advanced civilisation, the traces of which have been destroyed by glaciation, and the UFOs we see are their deep- space probes returning to report back....