Can I keep about 10 lbs of already grilled hamburgers warm in a roaster oven overnight. They will be submerged in beef broth......
It will be safe if the temperature is consistently above 140 F / 63 C, but it is almost certainly a very poor idea from a quality perspective.
If the temperature does not stay above 140 F, then you are incubating the hamburgers, inviting pathogens to grow: that is dangerous and a very bad idea.
Hamburgers are one of those items that are best served immediately upon being cooked; there is no really good way to hold them or reheat them and have the same experience.
If you have to have them cooked in advance, I would refrigerate them and then reheat with the method of your choice, such as in a moderate oven (for a large quantity).