I didn't try it with a table, so this answer might be of very little value for you. But it works in normal text.
Make a bookmark for the original (select it, than Insert>Bookmark and give it a name). If you want a copy, Insert>Field>Links and references and choose Ref with the name of the bookmark as a parameter.
You need to refresh the field for the value to show up on the screen, I'm afraid. But it surely is printed.
There might be better tools to make fillable forms, such as Adobe Acrobat. I don't know of any free ones, but I don't exclude they exist.
Hope this helps.
(Using MS Word 2002/2003)
BACKGROUND: I developed a multiple page form using tables. Near the beginning of the form I have a cell with the title "STUDENT NAME" followed by a blank cell where the student name is typed in by the user. At the top of each consecutive page on the form is "STUDENT NAME" followed by another blank cell where the name is typed in.
QUESTION: Is there a way to have Word automatically insert the name I typed in the blank cell on each consecutive page that follows? (I know this is possible in Excel)