The "weights" and the saturations of the colors have a lot to do with this. Brown, a dark neutral, should be able to support two bright colors: teal and red. If the teal is very prominent and bright, stick with a darker red. (Remember burgundy? It's a conservative neutral red, but you don't have to go that far.)
Add a neutral bag from the brown family that's lighter or darker than the brown in the dress.
hmmmm...red probably wouldn't be my first choice. I would pry go with orange, yellow, or a snakeskin neutral before red. I guess I'd have to see it together to really judge it, though.
Id say yes if the dress is a bright teal or a chocolatey brown(or any warm brown but if the tea is paler or the brown is "colder" try a very deep red or purple