Roundup is a non-discriminant herbicide, so you will kill the stump, and anything around it, and anything that might want to grow there in the future.

The WHO has linked glyphosate with cancer. This is not 100% verifiable, but I avoid Roundup because I'd rather have weeds than cancer.
http://www.pbs.org/newshour/rundown/roundup-ingredient-probably-carcinogenic-humans/

If you really want to kill it, just pour vinegar down its throat. I've also heard that drilling holes and pouring fertilizer into them can also kill it faster.