Absolutely possible. Start by reading
http://sbarnhill.mvps.org/WordFAQs/Letterhead.htm to get the basics of
setting up separate headers and footers for the first page and subsequent
pages.
Then put your letterhead in the First Page Header and whatever other content
you want in the primary Header that will appear on pp. 2ff.
Then you'll need an IF field in the footers. I'm assuming you want
"continued" on every page but the last, so you'll need the same field in
both First Page Footer and Footer:
{ IF { PAGE } = { NUMPAGES } "[Paste in your table here]" "Continued" }
This tells Word that if the page number of the current page is the same as
the number of pages (that is, if this is the last page), it should put your
signature table; otherwise, it will print "Continued."
To construct this field, you need to press Ctrl+F9 to insert a pair of field
delimiters (the things that look like curved braces but can't be entered
from the keyboard). Type the text between them, using the Insert Page and
Insert Number of Pages buttons on the Header and Footer toolbar to insert
the PAGE and NUMPAGES fields. For starters, I'd just type some placeholder
text for the table (as in the above example) so that the field doesn't
become unwieldy while you're working on it. Then set up the table as desired
somewhere, copy it, and paste it in to replace the placeholder.
The field will look very daunting, but F9 to update it (Alt+F9 if necessary
to toggle the display), and you should see your table on the last page and
"Continued" on all the other pages.
Note that after you have constructed this field in the Footer (or First Page
Footer), you can copy and paste the entire thing into the other footer, but
be aware that no matter how carefully you copy and paste, you'll end up with
an extra empty paragraph in the footer you paste into, and this will need to
be deleted. It's easier to be aware of this if you have nonprinting
characters displayed.