Math says YES, assuming out-migration at some fraction of the speed of light (c). This NASA page estimates a star density of 0.120 stars per cubic parsec (CP),

Math says YES, assuming out-migration at some fraction of the speed of light (c). This NASA page estimates a star density of 0.120 stars per cubic parsec (CP), where a parsec is 3.26 light years. http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980123d.html http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980123d.... Thus that page's estimate of the number of stars within a 100 light year radius of Earth is: = 0.120 stars/CP * 4/3 * π * ((100 LY)/(3.26 parsecs/LY))^3 = around 14,600 stars Recalculating for 1,000 light year diameter: = 0.120 stars/CP * 4/3 * π * ((1000 LY)/(3.26 parsecs/LY))^3 = around 14.5 million stars So given 10,000 years, and out-migration by Hansonian 'ems' (mental-simulations) at just 0.2c, and even starting more than a thousand years from now, many tens of millions of stars would be reachable. Of course, there are many other challenges with that prediction, but the speed of light is not an absolute barrier, as you suggest.