Very close to reasonable, yes. Proper dreadlocks do require some attention to establish, so that they will form 'tails' and not a giant matted mess. Once established, however, they are an excellent low-maintenance hairstyle and have been used by various cultures. That part should fit fine.

While dreadlocks are best known as a way of wearing nappy hair, they will also work rather farther down the scale. Very fine, straight hair usually won't lock properly but sometimes wavy hair will and loosely curly hair almost always will.

Do be aware that hair is a minefield, and ethnic hair even more than average. Even a quick browse will turn up examples. If you're sensitive to other people's tantrums, you might want to avoid this issue. Me, if people are already screaming at each other over something, I just pick what I think is reasonable and write it.