Maybe.
We all like to dream about super-fast interstellar travel, but barring a miracle, the speed they’re talking about is probably not likely to be improved upon very much.
On the other hand, 6,300 years is plenty of time in which civilization on Earth could collapse completely. In which case space exploration will come to a screeching halt while our intrepid colonists (and there descendants) are in transit.
Planning on that time scale is beyond us now. Maybe it won’t be a big deal eventually, if we figure out how to extend our lifespans. I read one sci-fi series where the aliens don’t bother to contact ‘primitive one system powers’ unless they can stick to a plan for 50,000 years or so if I recall.
Freegards
Based on size of Universe, whose end we have not seen yet because it is further than light could travel since humans appeared on earth, there are quadrillion**quadrillion planets out there in the universe.
Humans on earth will become extinct within a million years having endured 100 ice ages by then, but there will be human like creatures evolving in quadrillion planets somewhere in the universe.