Is it safe for the hard disk drive to operate while MacBook Pro is positioned vertically?
It is safe to operate the HDD this way. There are many servers that use HDDs vertically.

Your main concern, while operating this way, would be the slightly worse cooling. The Twelvesouth guys are saying that they deliver better cooling, but they are comparing it to a closed and put on the table notebook. My experience shows that the best way to keep the notebook cool is to keep the lid open. If I want to use only my external monitor, I close it, wake it with the external keyboard/mouse and then reopen the lid (only the external monitor works and the cooling is best). Note that if you're not doing CPU/GPU heavy things (gaming, transcoding movies), you'll be ok.