Is there a way to import a word document into InDesign CS4, including its headers and footers?
You have two problems with this. One is getting the header and footer copy into the text you are importing. You can do this if you save the .doc as plain text (.txt), although it will strip out the formatting and you'll lose any images.
The other is that InDesign doesn't know where to put the header and footer. You have to create text boxes for header text and footer text, preferably on the master page, and those text boxes aren't going to be linked to your body copy.
So the answer is no, you can't just place a Word doc into InDesign and have it replicate the header and footer text in placement and update page count and so forth. You have to create those manually.
(Additionally, although it's been a while since I worked in CS4, it doesn't look like you can place a .doc at all. You have to use some form of .rtf or .txt to import.)