As Stefan has pointed out, the header expands automatically with any amount
of text. It expands downward rather than upward, however; the header margin
specifies where the top line of the header will be. As a general rule, using
Word's default font, Header style, and margins (1" Top and 0.5" Header), you
can get two lines of header text before it starts intruding on the document
body. Anything more than one line will really be uncomfortably close to the
document body.
If you want to maintain a specified distance between the header and the
text, regardless of the depth of the header, the best plan is to add this
amount to the Header style as Space After, which will ensure that the header
paragraph will always (if necessary) push the document body down enough to
leave this space. If Space After is added to the Header style, make sure to
use line breaks rather than paragraph breaks within the header. Otherwise,
add the space only to the last line in the header.