You'll be fine if you're just planning to play through the story and PvE parts, up until about level 50 or so I reckon. If you don't want to spend any money you can buy gold-packs in-game (they are quite pricey though) and you can get the full benefit of the game without needing to spend a cent.
You won't be able to use the Trade Broker, so making money is going to be an issue.
