No. In general those comets known as Short Period Comets originate in the Kuiper Belt.
Long Period Comets (or those with orbital periods greater than 200 years) are said to originate from the Oort Cloud.
[edit on 21-4-2009 by Resinveins]
"Even though the comet itself came from way out past Pluto, there’s a much more complicated history of migration patterns within the solar system and the material originally may have formed much closer to Earth,” says UW-Madison geology professor John Valley. “These findings are causing a revision of theories of the history of the solar system."Source-Science News.
Early on, scientists found surprising evidence that Wild 2 contained some material from the inner solar system that had been heated to more than 1000° C due to its proximity to the Sun.Source-New Science.
Despite the comet’s birth in the icy reaches of outer space beyond Pluto, tiny crystals collected from its halo appear to have been forged in the hotter interior, much closer to the sun.Source-Science News.