Your question about whether water droplets burn leaves has been answered (it's "NO"), but here's something to think about. Mother Nature doesn't just send rain in the early morning or late evening. IF water droplets on leaves could cause burning, every time it rained and then the sun came out, everything green would soon be everything brown. In just the past two weeks here, there have been multiple afternoon showers where it has immediately cleared and hot, unfiltered, fierce sunshine from cloudless skies (I'm talking mid-to-upper 90's F) has beat down on...wet leaves...leaving nary a burn mark. One caveat: if your water is like mine, and high in mineral content (it's a miracle I don't have kidney stones, lol), when you spray your roses you might see some light residue on the leaves, especially if you end up making it a daily routine/regimen. The residue is harmless, and might even provide some "sunscreen".
I had just mentioned the other day on the "other" forum that anytime the temps here reach the mid 90's I start spraying my roses down. You can literally see the difference in a few days, and there's no worry about spreading BS, because at those temps the spores aren't active; not to mention the leaves dry in minutes! lol. Besides keeping the spider mites under control, the roses may even start setting buds again (mine did), whereas the plants had been in comas during the worst of the heat. After being sprayed down twice daily, my Prairie Peace (a spinosissima hybrid, rare as hen's wisdom teeth) even started throwing new canes this summer...out-of-season and almost unheard of since it's a "cold climate" rose; and that's after it's normal Springtime new canes had hardened off.
So don't be afraid to spray down your roses. Assuming you don't have water restrictions right now, the worst you can do is raise your water bill a bit, lol.
John