If you have knobbies or any slightly aggressive tread pattern, I'd change to slicks. The only thing knobs and large tread does is attach a chip seal road to your bike that wears you out quicker on smooth pavement.
My son road his first Century ride several years ago on a heavy Trek Marlin, he made it. But he bought a lighter road bike soon after. But I don't think your Diverge is heavy enough for weight to be an issue.