Yes it's possible, provided you have the application to do it (such as
Acrobat or one of the clones).

The method (for Acrobat) depends on which version you have. The actual
conversion is simple. (Set Acrobat as the active printer, then print the
document.) The hard part is preventing Acrobat prompting for the filename.
Some versions of Acrobat use a registry entry: set that to the filename and
you're done. Or you tweak the Acrobat printer settings so it doesn't ask;
the PDF then ends up in the same folder as the Word document, same name but
with PDF extension.