As I answered in a later question, it is possible that global temperatures will drop as a result of a volcanic eruption, as evidenced by the eruptions of Tambora in 1815 and Mt. Pinatubo in 1991, but it is not a guarantee. Other large eruptions, such as El Chichn in 1982 seemed to have little effect on global temperatures.

Given Mt. Redoubt's history of eruptions (which have the secondary effect of reducing pressure in the volcano), I believe a full eruption of Mt. Redoubt would be less likely to send ash and sulfur dioxide high enough into the atmosphere as to create significant global cooling as there is less pressure built up than in, say, a Krakatau.

Additionally, if a full eruption involves blowing out one of the sides of the volcano (as Mt. St. Helens did), ash and sulfur dioxide would also be expelled laterally, so less of it would reach the upper atmosphere.

Despite all these counterfactuals, however, it's still certainly possible that a full eruption of Mt. Redoubt could cause a temporary drop in global temperature; it's just less likely to do so than other volcanoes.
Source(s):
http://www.gsfc.nasa.gov/gsfc/service/gallery/fact_sheets/earthsci/volcano....
http://pubs.usgs.gov/fs/1997/fs113-97/fs113-97.pdf

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