Of course it is possible! I've worked with several turnkey contract manufacturers in the US that would be happy to build 100 circuit boards. Some will even do PCB layout and help with circuit design. Mechanically, places like protomold and quickparts are a good source at low volumes, especially if you can hand them a CAD file of the enclosure design.

If you're looking for someone to help you out, go where those people hang out: places like sci.electronics.design on usenet, Circuit Cellar Ink forums (http://bbs.circuitcellar.com/phpbb/), Embedded.com forums (http://www.embedded.com/tigforums/index.jspa?categoryID=1), and maybe even chat rooms like #edev.

If you're looking at less than 10k units, I doubt it's worth the effort to go off-shore.