No - in fact they (correctly) believed the opposite. At the beginning of the secession movement, most Southern seats in congress were controlled by Democrats, while most Northern seats were held by Republicans, who had close ties to the abolitionists. After emancipation, slaves naturally gravitated to the Republican Party, and all the early African-American politicians were Republicans. So emancipation hurt the interests that benefitted from the 3/5 compromise because African-Americans didn't vote the same way as white southerners.