History has provided us with a couple of inadvertent ash cloud 'experiments'.
In 1982 a British Airways 747 flew through a plume of ash thrown up by the eruption of Mount Galunggung south east of Jakarta. The aircraft was at 37,000ft when one engine failed. The crew performed the required engine shut down drills, but within a minute another engine failed with the remaining two failing just seconds later. The 747 was able to glide clear of the ash cloud, and at 28,000ft the crew made an unsuccessful attempt to restart the engines.
In an aeroplane the engines drive the pressurisation system, and as the cabin pressure decreased, the passenger oxygen masks dropped. With mountains between the aircraft and the emergency diversion airfield it looked like a ditching in the Indian Ocean was inevitable. Fortunately after losing over 25,000ft the crew managed to start one engine and then the other three (although one had to be shut down again). With sufficient power to safely reach the airport, the crew were still faced with the challenge of landing with windscreens that had become almost opaque thanks to the effects of the volcanic ash.
Seven years later in December 1989 a six month old Boeing 747-400, operated by KLM, was descending into Anchorage Alaska. While descending through 24,000ft the pilot flew through a cloud which turned out to be the ash plume from Mt Redoubt, an Alaskan volcano that had erupted the day before. As the the cockpit filled with what the pilots thought was smoke, the crew turned left and tried to climb out of the ash. Seconds later all of the aircraft's four engines shut down. The aircraft lost 14,000ft in height before the captain managed to restart at first one engine and then the others, the crew made an uneventful landing. As a result of ash damage all four engines were scrapped at an estimated cost of $80m.