Impossible. The stars would not be any more visible than they are on the surface. Perhaps even less so, as your pupils will be wide open for the low-light you are in, and the daylight outside will seem very bright...
There are some other neat daylight effects tho. On a windy day, with the sun shining but not directly visible out the entrance, a cloud passing over the entrance will actually brighten the interior of the cave, as it increases the amount of indirect light reflected back in...