I think that it's important to know how a thing works. I think that's true even for a period. A period isn't just the end of a sentence, but a metaphorical end. Celia Klin, of Binghamton University performed a study that addressed this question in regard to text messaging. She found that using periods at the end of a text were seen as more formal, and aloof, and those qualities were attributed by subjects in the study to the author of texts that used periods at the end of the text.
So, people perceive and use periods as a statement of finality and inflexibility. Knowing that, if I were to write a character that is persistently indecisive, or weak willed perhaps, I'd use no periods, and break each thought into it's own speech bubble. Most readers wouldn't realize it, but the science suggests that they would feel the difference in tonal quality and personality of the character.