GDP is more akin to a Country's income rather than wealth (for simplicity: the sum of all salaries and corporate profits generated by the country's residents, either physical or legal entities; imports and exports of goods and services have an impact too but let's ignore it for the sake of simplicity). So the similitude with Bitcoin would be with the added coins in one year.
Just for some reference. In 2016 Italy had a GDP of 1.8 Trillion USD, 2.5% of Global GDP, close to the 2T of comments here (
https://en.wikipedia.org/wiki/List_of_countries_by_GDP_(nomi... ). In 2012 it had share of 1.5% (321 / 20,900 PWh) of total electricity power (
https://en.wikipedia.org/wiki/Electric_energy_consumption , let's assume that share has not changed much since 2012).
Global GDP growth is around 3.5% in 2016-17 (a bit more than 1.5 Italies get added to the Global economy).
Broadly speaking, Central banks today feed this growth by printing money (i.e. increasing the money supply), hence inflation. A deflationary currency like bitcoin would have to grow in unit value accordingly because of its cap, if it were to become the de-facto new gold standard. How much power consumption is appropriate for mining needs to be considered in relative terms vs how much mower hungry is gold mining, for example. I am not sure how power hungry is printing and managing cash (incl. security, transport...).
Also, all these activities (gold mining, bitcoin mining, cash printing) also contribute to GDP. Eventually if the power source is renewable and generation capacity is kept at appropriate level (e.g no one dies of cold because power must be prioritized to mining) does it matter? Or am i missing something?