It's your bike. You can put whatever you want on there that feels good to you. In my early years I would put baseball bat grip on my tennis racquets for example. That's probably more ridiculous that your question.

If you put bar tape on your bars and the bar ends, you'll need more tape than what they would supply with the bartape. For a mountain bike, I suggest running either some very thin double-sided tape, or electrical tape sticky-side up under the bar tape to keep it in place. Go to the Park Tool website for other tips on wrapping bars.