I have a couple of roses in containers. I was thinking of putting some succulent mix, perlite, or decomposed granite on the surface of the potting soil in the rose containers and planting some succulents there and letting them spill over the edge of the pot. Do you think that would work?

I would not mix different kinds of soil, but as long as the soil is the same throughout the pot, I think it would work well, as long as the rose isn't too big and blocking too much of the lower light.

Do you have any particular plants in mind? Are you able to add a pic of the containers?

You might want to ask this on the Rose Forum and get some opinions from there.

You would have to get succulents that could handle the amount of water you would need to give a rose.

Roses, especially in pots, need lots of water, succulents not so much. Not a good combo IMHO. Maybe something like alyssum would do nicely.

"surface succulents" have worked wonderfully for me in many group planters without changing the soil...
I live in NY, and I've had succulents growing around mature hibiscus, pineapple and Canna

You can top dress the pot, but be careful about layering soil types... I wouldn't do it. You don't change the soil, the right way to do it is pick the right pot.
a large pot will automatically stay moist toward the center and bottom... most succulents have very shallow roots, so you can let the pot top dry without Stressing the deeper more water dependent plant.

I don't think you can do it laying different substrates- you'd never know what the middle looks like, you'd likely rot the center if you layer different draining soils. You can do it by selecting pot size/shape. A deep pot is better than a shallow pot, wide better than narrow.

The one thing I assumed is that this will be an outdoor full sun- as your roses and succulents both want- so that the sun will dry the top inch nearly daily. is that accurate?

That's what I see in mixed pots. I have quite a few of them with all kinds of strange bedfellows.