Not really.
First, both the US and other developed
countries got that way with "moderately expensive" energy, not cheap
energy. Oil and electricity have been cheap in the US in the post-WWII
period, but energy was rather higher in years before that: coal and
electricity cost much more, adjusted for inflation. The US, and other
countries, succeeded quite well in growing strongly even when energy was
much more expensive, whether it was coal or oil.
Wind
power is quite affordable (if perhaps not quite as dirt cheap as US
post-WWII oil and electricity prices), scalable, high-E-ROI, etc, etc.
So are nuclear, and solar even if they aren't quite as cheap at the
moment (coal is also plentiful and cheap, unfortunately), so I see no
reason to expect energy to ever be more than "moderately expensive".
The
fact that energy pre-WWII was a much higher portion of GDP means that
it was a much heavier burden on the economy. If wind and solar are a
little more expensive, that means that the wind/solar sector has to be a
little larger than otherwise to power the rest of the economy. This
analysis suggests that this is not a big deal: that sector would still
be a much smaller portion of the economy than pre-WWII.
Second,
fossil fuels aren't nearly as cheap as they seem. Pollution is an
unrecognized, external cost. So are the military costs we're seeing
currently of roughly $500B per year. Those pollution costs aren't
sustainable (especially CO2), but unfortunately the military costs
of security for oil supplies probably are (in fact, many corporate interests are quite comfortable
with them...). Not that they don't entail many costs to the economy, including diverting
scarce scientific and engineering talent away from creating new products, and growing the economy. Moving away from oil and other fossil fuels will actually
be much cheaper in the long-run than BAU.
Finally,
let's assume that Business As Usual involved spending about 5% of our
economic activity (perhaps measured by GDP) acquiring energy. If the
cost of acquiring energy doubles, then we have to dedicate another 5% to
that activity. GDP might go down by 5% quickly, in case we'd have a
deep recession. Or, it might happen over time - if it took 10 years,
then we'd see a reduction in economic growth of .5% per year, for 10
years. After that transition was complete, economic growth would
continue. So, a reduction in "net energy" has a significant impact, but
it's not TEOTWAWKI.
Does unusually strong growth since 1945 show the value of cheap energy in that period?
No, US growth was faster before 1945, using moderately expensive, non-oil energy:
1800-1900: 4.13%
1900-1945: 3.53%
1945-2000: 3.17%
"real GDP" at http://www.measuringworth.com/growth/index.php