Yes. You don't have to have either, you can bounce the flash. It eats up more power from your flashes, which isn't a big deal really (I use 2 quantum turbos in addition to carrying like 30 AA batteries with me).
What the softbox/umbrella does is it softens the light and creates more balanced lighting. For portraits, it's nice to be able to control that. Also, don't forget the cheapest light modifier out there, reflectors. A single bounced flash with a reflector and some ambient light works really well.