The tank that you said is 11"x7"x7" is not 2g it is 1.8 which makes 0.9g each. That is if you fill this tank to the brim, not accounting for water displacement by heater. As someone else has said in a divided tank the bettas need to be able to escape each other in a cave or somehting but in a tank this big you wont have space...
So you have to ask yourself, do you really want two bettas or do you want to do the best by the fish? One gallon is the BARE minimum. 2 or 2.5g is a lot better. You can keep a dog in a cupboard and throw in a bone once a week, it'll live but doesnt mean it would be happy. Only take on what you can handle and afford. Its only right by the fish.
Also this would mean you would not have space for a heater, so you would have to do 100% water change a week. Would you be able to keep up with this?