There are charcoal pellets available for use with pellet smokers. Pit Boss sells a charcoal/wood blend. Royal Oak sells 100% charcoal pellets. Charcoal burns hotter than wood pellets, so there could be issues with temperature control.
I was part of the gas grill crowd and much prefer the taste from the Traeger. I never liked charcoal fired grills because they are so messy to clean up and the temperature had to be maintained manually. While you won't get the same flavor with Traeger that you got with your Weber Bullet smoker, it will be a lot more user friendly during the cook and cleanup is much easier.
Check out some of the threads on smoke tubes which many people use to enhance the smoke flavor.
Some enterprising Traeger owners have modified their grills to use a cold smoke generator such as the Smoke Daddy or Smokai to have real wood smoke flavor in a pellet grill. However, such modification does require drilling a hole in your grill chamber.