Is it possible to convert a PDF into a Word document without Adobe Acrobat?

Yes it is.

http://convertpdftoword.net/

http://www.pdfonline.com/pdf-to-word-converter/

there are other PDF readers than Adobe. Foxit Pro for one I think.

On Linux there's pdftotxt in poppler-utils which makes plain text from PDF which you could then import into OpenOffice.

Or you could "convert" a PDF by taking a snapshot and inserting it as an image. Some PDFs are images anyway.

Yes it is ... get Adobe Reader .. which is free

http://get.adobe.com/reader/

open the document and say export to word document .. or you can just save as text

either way will do

If this is a mass conversion and you are tech savvy you could make a C# program . i have one with code already done if you are able to use it