The culprit is atmospheric carbon dioxide (CO2), which even in a cooler globe will continue to be absorbed by seawater, creating acidic conditions.
"There would be a slight reduction in this problem, because land plants would be expected to be able to grow more vigorously in a high CO2, but cool world," said Ken Caldeira of the Carnegie Institution's Department of Global Ecology.
Land plants and soils would hold onto more carbon in this scenario, so less would find its way into the oceans.
"However this expansion of the land biosphere, while it's a slight help to ocean acidification is not enough to make a big difference," said Calderia.
A widely-discussed proposal for countering warming with geoengineering involves injecting small, reflective particles into the upper atmosphere.
This would partially block incoming sunlight before it reached the Earth's surface, lowering global temperatures just as volcanic ash from the Mount Pinatubo did following its eruption in 1991.
But, critics have warned that such a scheme might also alter rainfall patterns, damage the planet's ozone layer, or have other unexpected effects.
Until the current study, which used a computer model of the Earth's climate system and biosphere to simulate the effect of geoengineering on climate and the ocean's chemistry, the potential impact of such a scheme on ocean acidification had never been calculated.
In the simulations, reduced sunlight cooled the planet as expected, and it also slightly slowed the rise in atmospheric CO2, as natural sinks absorbed more carbon.
But, this slight change was not enough to significantly mitigate ocean acidification.
Ocean acidification rivals global warming as a threat to marine ecosystems, especially coral reefs, which need to be surrounded with mineral-saturated water in order to grow.
Rising levels of carbon dioxide make seawater more acidic, leading to lower mineral saturation.
Recent research has indicated that continued CO2 emissions will cause coral reefs to begin dissolving within a few decades, putting the survival of these ecosystems at extreme risk.
"Geoengineering approaches come with all sorts of risks. It is important we learn about the the full set of these risks and all of their implications," said Caldiera.