Yes you can, you have the choice of keeping the Sword of Aeons by just walking out of the Guild doors, it is not a good or evil choice.
Another way is to "hero Save" after beating Jack Of blades then Quit. You should then have the Sword to fight Jack for the second time, and when you choose the benevolent decision, you will still have the Sword of Aeons, and you will still be able to get Avo's Tear and have both swords. However, this can also result in weilding a stick upon reloading, and not having the Sword of Aeons in your posession.
Of course, if you want to be good throw the sword into the vortex. In The Lost Chapters you can get Avo's Tear, a sword with stats as good as The Sword of Aeons that you can only get if you don't have The Sword of Aeons.