No. Just wipe off the excess.
Are you talking about the sliding joint in the middle of the shaft, or the U-Joints ?
Since the driveshaft is open, any excess will be flung all over the back of the motorcycle and leave a mess to clean up.
But that's just a day in the life of a Spiney. The drive shaft and U-joints on my Sport 1100 is always caked in grease.