Not necessarily. Armour is there to save you from cutting, penetration or blunt trauma. A weapon like a sword must have the right properties like being able to keep a good edge, right weight and the possibility to balance it properly etc. Kevlar is great for stopping bullets in real life, but that doesn't mean that a kevlar knife or a kevlar bullet is a winning concept.
Also makes me wonder just how would a dragon bone sword look like. Generally it would be possible to stitch or otherwise fix separate dragon scales/bones together for armor, but it's not like you can melt them and forge a sword out of it. Dragon bone warhammer or even axe are possible, but a sword? It would probably look like http://en.wikipedia.org/wiki/Macuahuitl, i.e. not that hot.
