gdp growth =/= energy consumption growth
Also 1.03^1000 = 6.810^12, but wolframalpha says the number of stars in the milky way is 310^11. Considering that we're nowhere close to capturing even 1% of the energy output of energy that reaches the earth, let alone all the energy that the sun emits, your estimate of 1000 years is probably off by a few orders of magnitude. Finally, if we're actually capturing all the energy of the milky way, presumably we'd be a space faring civilization and can therefore colonize other galaxies, making that a non-issue.