Correct. Plantation owners wanted to be able to cast hundreds, perhaps thousands of votes for their candidate of choice by bundling the votes of their slaves. Granting full suffrage to slaves would also have greatly increased the slave states' position in the Electoral College. The ugly truth is that there was no suffrage for slaves until after the Civil War. Southern slave owners cast votes on behalf of their slaves, albeit only 3/5 of them.
As I recall, the 3/5 rule did not apply to slaves having a vote, nor the slave-owners casting a vote for them.
Instead, it applied only to the census enumeration. Slaves were counted as 3/5 of a person for the purpose of apportioning Representatives. As a matter of course, this also impacted the Electoral College.