Depends a lot on timing ..
If it's early (1862 or so), it's possible that Hamlin and Congress might have trouble staying the course through the dark times.
Once you get past Gettysburg and Vicksburg, then the course is largely set. Hamlin would continue the course.
Once you get to Johnson, the course is still set for victory, but he would have begun working for the quick restoration of CSA states, with Democrat governments and with no protections for freed blacks of any kind.
What if Lincoln had been assassinated by Southern sympathizers like John Wilkes Booth earlier in the Civil War during 1865?