Even if the EmDrive works, it’s most likely we will need to first achieve immortality (or at least significantly extended human lifespans) to leverage it for interstellar travel.
Barring the discovery of a new quirk in physics that permits superluminal speeds, transit times to any planets outside of the solar system will be measured in at least years, if not decades or centuries. Exploration to find worlds either suitable for habitation or capable of being terraformed will take centuries due to the sheer distances involved.
An EmDrive would be perfect for local travel within the Solar System and it could make the colonization of Mars, for example, a feasible endeavor. It remains to be seen whether Venus could be altered sufficiently to make it suitable for carbon-based life.
Of course, there is always the popular science-fiction approach of constructing self-sufficient, multi-generation arks and tackling the time/distance/relativity challenges that way but that raises an interesting question. If we can create a viable habitat, why bother looking for new planets? Given that we already know of a number of extra-solar planets why not just use them as “supply depots” for replenishment and expansion of the habitat? After a few generations, the memories of planetary existence would be less influential and the “ark” would be the familiar environment.
Moreover, the chances for species survival would be enhanced by the construction and deployment of multiple habitats that are not subject to planetary and solar forces. Unlike the Earth, which is at the mercy of whatever rocks the universal cares to toss at us, a habitat, even a very large habitat, would be able to simply move out of the way.
The EmDrive, or something fairly close to the concept, would make such a diaspora not only possible but quite likely inevitable.
Incidentally, true “immortality” is probably impossible as it postulates the survival of the energy death of the universe. We would have to take Voltaire’s dictum about God seriously and create a transcendent humanity.