Is the Iceland volcano part of the glacial cycle?

Following up on this article.

The problem here is that at the height of the ice age, that region is covered in ice and the plates severely depressed by a ten to a hundred of feet. As the ice melts, the pressure release and the volcanoes burst. The subsequent global soot would cause cooling,. This theory explains a lot, actually though I am not ready to believe it.

And this:

OSLO - A thaw of ice caps in coming decades caused by climate change may trigger more volcanic eruptions by removing a vast weight and freeing magma from deep below ground, research suggests.

While that's not the case with Iceland's Eyjafjallajokull glacier, which is too small and too light to affect local geology, other volcanoes on the island nation are seen as vulnerable.

"Our work suggests that eventually there will be either somewhat larger eruptions or more frequent eruptions in Iceland in coming decades," said Freysteinn Sigmundsson, a vulcanologist at the University of Iceland.

At high pressures such as under an ice cap, they reckon that rocks cannot expand to turn into liquid magma even if they are hot enough. "As the ice melts the rock can melt because the pressure decreases," Pagli said.

The chart above is the glaciaL cycle. The problem has always been explaining the sudden shift beck to an ice age. Theories considered are the sudden release of water, a sudden freeze over and albedo effect (sun reflection, or asteroids. The asteroid theory is interest because it includes a layer of soot. Anyway, volcanoes have now become a strong suspect, and the probability of a reversion to an ice age must be higher in our calculations.

One more from Iceland:

Katla volcano, located near the southern end of Iceland's eastern volcanic zone, is hidden beneath the Myrdalsjökull icecap.

The subglacial dominantly basaltic volcano is one of Iceland's most active and is a frequent producer of damaging jökulhlaups, or glacier-outburst floods. A large 9 x 14 km subglacial caldera with a long axis in a NW-SE direction is up to 750 m deep. Its high point reaches 1380 m, and three major outlet glaciers have breached its rim.

Although most historical eruptions have taken place from fissures inside the caldera, the Eldgjá fissure system, which extends about 60 km to the NE from the current ice margin towards Grímsvötn volcano, has been the source of major Holocene eruptions. An eruption from the Eldgjá fissure system about 934 AD produced a voluminous lava flow of about 18 cu km, one of the world's largest known Holocene lava flows. Katla has been the source of frequent subglacial basaltic explosive eruptions that have been among the largest tephra-producers in Iceland during historical time and has produced dacitic explosive eruptions during the Holocene.