Prufrock is really supposed to represent modern man; his thoughts, while seemingly unconventional in the way they present themselves on the page, really are not. Are his thoughts much more fragmented that our own? His thoughts may move from one to another, but they do so in a way that mimics our thought process. Prufrock moves from one doubt to another, and his seemingly random observations are rooted in his past and his insecurities, just like ours are. This poem's fragmentation does serve to display Prufrock's indecisive, second-guessing, and pessimistic nature, but it more importantly mirrors the fears and uncertainties we all posses. He is the quintessential modern man, and his fragmented and often unsure voice is proof of it.
A very focused question. I would describe the poem's use of the theme of fragmentation as somewhere between symptomatic and definitive. By that I mean, both Prufrock and his world are fragmented. He can't really connect with the women he sees, the conversations he hears, the city he walks through, or the mermaids he hears. The fragmentation in the poem—the worries, the interruptions, the repetitions—all sum up his relation to the world, and communicate a sense of it to us as readers.