Well, I definitely couldn't (I tried them once and felt like Bambi) but I have friends who do. Watching them wear them for the first few times is usually quite funny 
I wear 2 1/2" for both, and that seems pretty standard, although some people choose to wear a slightly lower heel for ballroom.
Most men wear 1.5 or 2 inch cuban heels for Latin, and you don't want your partner in higher heels than you...