Can oil/grease damage tires?
Like Daniel said, a good rule of thumb is to keep oils off rubber and plastics. Some will damage them, some will preserve them, but you don't want either type on your tires. You should be more worried about the fact that the oily spot on your rear tire can cause it to break traction much more easily, especially while braking or cornering. If you're going to be storing the bike for any period of time, just stuff a rag between the spokes up next to the hub to catch and absorb the oil.