Yes it can. When the document is open, tap the wrench icon in the upper right corner. In the next window select either Email Document or the Open In Another App or even the Copy to iTunes option. In the next Window that pops up - you can export the document as a Pages, PDF or Word document.
From there you will have to email the file, open it in another app or copy it to iTunes and the use file sharing to transfer it to your computer, but I would assume that one of those options would fit into your plans anyway.
If you wanted to save the doc as a Word file and still keep it in Pages, you can email it to yourself after exporting as a Word file as described above - and then use Open In - in the mail app - and save it back to Pages as a Word file.