The ejecta and their momentum appear to be entirely the product of the dissolved gasses in magma, according to this page on Physicochemical Controls on Eruption Style on the How Volcanoes Work pages of the Geology Department of San Diego State University:
The amount of dissolved gas in the magma provides the driving force
for explosive eruptions. The viscosity of the magma, however, is also
an important factor in determining whether an eruption will be
explosive or nonexplosive. A low-viscosity magma, like basalt, will
allow the escaping gases to migrate rapidly through the magma and
escape to the surface. However, if the magma is viscous, like
rhyolite, its high polymerization will impede the upward mobility of
the gas bubbles. As gas continues to exsolve from the viscous melt,
the bubbles will be prevented from rapid escape, thus increasing the
overall pressure on the magma column until the gas ejects explosively
from the volcano. As a general rule, therefore, nonexplosive eruptions
are typical of basaltic-to-andesitic magmas which have low viscosities
and low gas contents, whereas explosive eruptions are typical of
andesitic-to-rhyolitic magmas which have high viscosities and high gas
contents.
A similar description is offered by Stephen A. Nelson, associate professor in the Department of Earth & Environmental Sciences at Tulane University:
At depth in the Earth nearly all magmas contain gas dissolved in the
liquid, but the gas forms a separate vapor phase when pressure is
decreased as magma rises toward the surface of the Earth. This is
similar to carbonated beverages which are bottled at high pressure.
The high pressure keeps the gas in solution in the liquid, but when
pressure is decreased, like when you open the can or bottle, the gas
comes out of solution and forms a separate gas phase that you see as
bubbles. Gas gives magmas their explosive character, because volume
of gas expands as pressure is reduced.
So the gross extrusion of magma from the earth is not innately gas-dependent (though gas influences the composition of the magma), but the violent processes are caused more by gas coming out of solution and forming pressurized bubbles than gas or magma being under pressure, if that makes sense.