It's possible, but it might be difficult and more error prone. This is a big decision and effort. I would want to do research, plan the implementation project, create custom templates, etc. Depending on the existing day-to-day workload, I wouldn't want to do this type of implementation in less than 6 months to a year, and preferably only as a pilot project at first.
-- You can script things in Word with VB for Applications -- IF you have the skilled resources.
--Word has a lot of powerful features that are needed for documentation.
--Everyone has a copy in most organizations.
--Your documentation is already in Word.
--Word DOES NOT lend itself to separating style from content -- at least not without contortions.
--Word gets unstable when working with large documents and a lot of embedded and interlinked objects.
--Word output to HTML is problematic -- non-standard, can be ridiculously complex and use stylesheets (CSS) in the least-efficient ways.
--Word is not a content management system.
--Word does not allow simultaneous editing on a file by multiple people.
--Word does not have version control/source code repository functions.
FrameMaker is an alternative, but is also pricey.
I'm personally doing single-sourcing with HTML using the MS Web Expressions editor and using FAR Help tools to create online Help from the HTML. Then, using some custom tools and good-old hand-editing to turn the HTML topics into PDF manuals.
As a long-time documentation specialist, I'll also just point out that few writers and editors want to work this way; it's always management that thinks documentation can be made entirely efficient by not "duplicating" content and by "push-button" output to multiple formats. Except that well-made, usable and useful documentation is written for a specific media, format and audience, and is edited and formatted and produced specifically for that purpose; it is not done by pouring words into containers and using some code to re-purpose all the paragraphs by running them through templates. Watch out for all efforts to reduce writers and editors to automated routines, and to reduce all information to "re-usable" "content."