We surely would. But the gains may be more (or less) than you think.
I remember a gerontologist showing some math where if you prevented all heart disease you'd only gain about 4 years of human lifespan (since most of those people would soon get cancer); similarly if you prevented all cancer you'd only get about 4 years as well (since most of those people would get heart disease).
But if you prevented both, you'd get something north of 10 years of average lifespan.
