Even without mass conscription, the economy of colonies around the battlefield should be hampered, because the citizens at those places would left their daily job to manned the defense parameter. And that alone would greatly effect the economy
Plus conquering a planet need more than just 100.000 soldiers. They need millions. So how could there is no conscription? Unless the Dominion war is not as big as we think, and there is no planetary siege at all. But... a war of a galactic scale? What do you think about it? Even world war II push the US government to conscript their people. And it is only a planetary scale of war. Not a galactic one.