Is There Evidence Aggregate Demand Played a Role in EZ Crisis?

Yes, there is:
Screenshot (48)
This is a scatterplot of Eurozone countries. Horizontal axis is change in RGDP over period specified in the data; vertical axis is change in the GDP deflator over period specified in the data. Periods specified in the data are variable, and are meant to approximate the timing of the last Eurozone recession in each country, or, if no secondary recession hit the country, slowdown after 2009-10 recovery.
Data here and is entirely from the St. Louis Fed fred2 site. Any errors are mine.
Note, if you remove Austria, Estonia, and Greece, the R-squared falls to .0538, not nearly as impressive.
An explanation: if aggregate demand did not play a role in the Eurozone double-dip recession (2011-13, generally), there should have been no correlation of decline in RGDP and growth in the GDP deflator during that period. If the major role was due to aggregate supply, there should have been a positive correlation of decline in RGDP and growth in the GDP deflator. As you can see, that is clearly not the case.
However, note that the largest gap between changes in the price level and changes in Real GDP occur in Greece, Portugal, and Italy-the three countries most strongly affected by the Eurozone crisis in terms of Real GDP, while Estonia, France, and Germany, which did not suffer nearly as much in 2011-13, have the smallest gaps between changes in the price level and changes in real GDP. For some reason, the entirety of the Eurozone is suffering from really sticky prices, with none having a rate of RGDP change higher than the rate of GDP deflator change. Price and wage controls in Portugal, Greece, and Italy would probably help alleviate their situations, as these countries have no sovereign monetary policy, and must rely on falling prices to combat the money illusion if NGDP falls. Note that regaining competitiveness via internal devaluation is not necessarily the issue here; trade is not a huge component of the Greek economy (gross exports only constitute about a third of GDP; net exports far less).