After the surgery, Ulric should have had 1 human life + 8 cat lives, adding up to a total of 9 lives.

We then see him die from (1) gunshot to the head, (2) drowning, (3) hanging, (4) car crash, (5) electrocution, (6) arrow to the heart and (7) stab wound.

It doesn't matter if he didn't receive all 9 lives of the cat (like the doctor said). He still had the cat's 8 extra lives added onto his 1 human life. So yes, he did have 9 lives, and he should have been able to survive the burial at the end.