If you increased our energy consumption by 1 % per year, we would all be dead in less than 1000 years because at that point the surface temperature of the Earth would have reached the boiling point of water.
EDIT: In case the down votes are for the numbers. The total emission of an ideal black body with surface area of 510.1 million km² at 373.15 K is 560,791 TW. The world total primary energy supply in 2012 is estimated to have been 155,505 TWh which is 17.75 TW on average. That is a factor of 31,591 from what Earth could radiate into space at 100 °C or 1,041 years of 1 % growth per year.
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.
EDIT: In case the down votes are for the numbers. The total emission of an ideal black body with surface area of 510.1 million km² at 373.15 K is 560,791 TW. The world total primary energy supply in 2012 is estimated to have been 155,505 TWh which is 17.75 TW on average. That is a factor of 31,591 from what Earth could radiate into space at 100 °C or 1,041 years of 1 % growth per year.