If we increased our energy production to 20000 times our current production (roughly 1000 years at 1% growth), I highly doubt we would still be stuck on Earth.
Leaving Earth does not really help that much - the number of stars and planets you can reach only increases with the third power - assuming an homogeneous distribution - and after some time more like with the second power due to the flat shape of the Milky Way and is in consequence quickly overwhelmed by exponential growth. You would not really get that far from Earth before you would already have to consume all the resources of the galaxy assuming some constant rate of growth on the order of 1 % per year.