I do not think these two events were related. Iceland eruption strained already limited European resources that were result of Seven Years Wars (1756-1763). After this war was over, European Continent suffered with poor harvests that lasted till 1773 and where up to 1/6 of population in many countries died from hunger. The famine ended suddenly with good harvests which caused population boom, and a huge dissatisfaction with the government. Austrian monarchy experienced its own version of peasant war in 1775 (caused by extremely good harvest, the best in the 18th century). Instability in France lingered till French Revolution. French Revolution was driven by population who lacked economic rise and means (too many people fighting fro finite resources, jobs, and positions). During the Thermidor coup in July 1794, temperature in Paris and Europe soared to 100F. Napoleonic era was known for its warm weather. The fashion of Directory till the end of Napoleon was very light with emphasis on silk.
The Second Awakening was more or less an answer on European anticlerical movement originating from Jacobin France. France had until 1805 colonies in Northern America, and many French lived there. French military agents recruited there among settlers, and there were Jacobins clubs in USA. Whiskey rebellion in Ohio valley is believed to be incited by French government to pressure Americans to side with them against Britain. Jefferson was admirer of French culture and society, so for many deeply religious people, it would create adverse effect and seek out new religious zeal. Remember between 1789 and 1800, France executed thousands of priest, and Napoleon even arrested pope, which was unprecedented act in European history.