Well, no, not exactly.
Initially, northern delegates drew up that representation should only account for freed men, which makes sense because without the compromise, the South would’ve garnered even more power based solely on population alone.
However, if the north truly wanted to curb the slavery, it could’ve no made any compromise at all. The South wanted it both ways. They wanted their population to count to total number of representation DESPITE the total population not being free. The South still got just that only slightly reduced.
In 1793, for example, Southern slave states had 47 of the 105 seats, but would have had 33 had seats been assigned based on free populations.
In 1812, slave states had 76 seats out of 143 instead of the 59 they would have had; in 1833, 98 seats out of 240, instead of 73.
It was a lose/lose, not a win/win for southern and northern states… supposedly, an identifier of a good compromise.
While southern states did not hold a majority, they still retained a significant voting block that allowed them to retain a pro-slavery influence over the federal government. They would’ve had less seats, not more seats, without it.
The perspective that southern states would’ve had more representation without it is a southern viewpoint and portrays the inherent view of the modern conservatives who align more with Southern Democrats than they do with the initial Lincoln Republicans.
Lincoln Republicans, if they had existed around the time the 3/5ths compromise had been drafted, wouldn’t have comprised at all and would’ve been in favor of reducing southern representation even more.
The only relevancy it had in terms of the civil war was that it was a moot point after the Union won. And the compromise was repealed. It held no significance in diminishing anti-slavery influence but allowed pro-slavery influence to even continue.
In short, it put off the Civil War. It did not reduce or increase the guarantee of victory over abolishing it.