It would be ok to put a sealant on. If you want to polish it to get scratchs I don't think a paint polish or compound is going to do much on the very hard grainte. To polish granite you sould really use a wet polisher with diamound polishing pads made for stone. They make pads with various grit sizes of industrial diamonds embeded in the pads for the job. Here's one the I have.
If you had the pads you might be able to use them with a UDM and a 4" backing plate if it has enough power. The pads velcro on just like a normal polishing pad. You could use sponge and water to keep the granite wet on cool. My wet polisher has a hose attachment and water comes out the hole in the middle of the pad. To polish the stone you have to go through the various pad with the different grits. I have pads going from 60 to 8500 grit. They are some people selling the pads on ebay.
I usually put Wolfgang Deep Gloss Paint Sealant on my granite. I usually just do it by hand but you could use your UDM.
