No, it's definetly not gumbo with rice cooked in it. I've never heard of making a roux to cook the trinity for jambalaya. I've never heard of roux being used in jambalaya.
OK here's what jambalaya is to me (learned from my mom's side of the family in NOLA [Gretna actually])
No tomato kine
3 cups or so of diced onion (more is better)
1 cup diced green bell pepper
1/2 cup diced celery (optional - debateable)
1 head of garlic - minced
1 lb cooked chicken meat, cubed
1 lb andouille, sliced 1/2" thick like peperoni for pizza
3 cups uncooked rice
6 cups stock (chicken, pork, turkey...)
several bay leaves
cayenne to prefered heat level
salt to taste
1 cup of chopped green oinions
Put 1/2 cup of vegetable oil in a dutch oven and heat over medium fire. When oil is hot add the onions, bell peppers,(celery), 2 teaspoons of the salt and 1 teaspoon of the cayenne. Stirring often, brown the vegetables for about 20 minutes, or until they are caramelized and dark brown in color. Add the sausage and cook, stirring often for 10 minutes, scraping the bottom and sides of the pot to loosen any browned particles. Add minced garlic, bay leaves and cook 2-3 minutes. Add rice and stir well allowing rice to become coated with, and start to absorb juices (this is the important part to making the rice taste right). Add stock, and chicken, stir well, cover pot and bring to medium boil for 10 minutes. Remove from heat and allow to sit with cover on until all of the liquid is absorbed (30 minutes or so). Remove the bay leaves. Stir in the green onions and serve.
If you use store-bought stock you can probably leave out the salt.
leave out 1 cup of stock and add one 14oz can of stewed tomatoes at the same time you add the stock.
There is debate about whether celery should be used or not. I like it better without, but that's my preference.
Jamalaya is really a catch-all for leftover meat. I've made it with every kind of meat imaginable. Something with fat (sausage prefered) should be cooked between the caramelized onions/peppers and the rice addition to make juice to coat the rice. This is a very important step for making the rice taste right.
EVERYBODY has there own take on this. Just like EVERYBODY has their own take on fried rice here in Hawaii. My Hawaiian friends love my jambalaya (they call it my 'haole kine fryrice")