Yes it does. Let us look at a concrete example in order to get the point. The EU plans to improve its energy efficiency by 20% by 2020. In other words, 20% less energy will be used by then, according to plans. The baseline is the primary energy consumption for 2010 which was 1770 Mtoe. Thus, if all measures are in place, by 2020 this figure should be down to 1416 Mtoe.
In all likelihood, the savings will concern almost exclusively the use of conventional energies (coal, nuclear, oil) whereas renewable energies will not be touched by this development. Therefore, we may safely assume that on the consumption side renewables will be equally well off as they are now. In fact, this is a very conservative estimate. On the contrary, renewable energy use may well be expected to rise over the next decade. But let us stick to our conservative approach for the time being. In 2010, the consumption of renewables amounted to some 172 Mtoe corresponding to 9.7% of total consumption.
Given our 2020 scenario from above and keeping renewable consumption at 172 Mtoe, we may conclude that by then renewables account for about 12.2% of total consumption. Bear in mind that this is true even if energy production from renewable sources does not increase.
The projection for 2020 would consequently look like this.
Thus, by saving energy the relative weight of renewables in the energy mix is automatically increased. The bigger the savings on the one hand the bigger the extra share of renewable energies on the other.