Even if you don't do the Battledome thing, Battledome related items can play a part in your Neopian life.  You will sometimes receive codestones, dubloons, bottled faeries and weapons as random events or prizes.  They can be sold, auctioned or traded like any other item.  So if you get one of these things, don't think they're no use to you.  Check the Shop Wizard for prices and make some neopoints from them.  Codestones, dubloons and bottled faeries are always in high demand.  If you price them competitively they will sell very quickly.

Another way to make neopoints from Battledome items is to stock up on them when the prices are lower between wars.  When rumors of a new war begin, the prices of battle items begin to rise.  By the time the war arrives some of the prices will have risen very dramatically.  This would be long-term investing, but the profits could be considerable.  Some good items for this purpose are: