OpenOffice can open Word documents and save as PDF. OpenOffice offers a special server mode for remote control.
Some information can be found here How can I use OpenOffice in server mode as a multithreaded service?
Update:
One way to do it is calling JODConverter
java -jar lib/jodconverter-core-3.0-beta-4.jar test.odt test.pdf
(note that even if this refers to Java, it is possible to execute this line from Delphi ;)
The page jodconverter Getting Started page at http://code.google.com/p/jodconverter/wiki/GettingStarted gives additional information, for example that OpenOffice starts in server mode, opens a port 2002 which then can be used to transfer conversion jobs. It also mentions a web application, which could be used from a Delphi client.
With the help some Java developers, this could be used to build a solid document converter, without the need of reinventing the whole wheel in Delphi.