The triad segments of Pages header and footers are not table cells, so are not resizable in a table metaphor sense. Text entered in any given segment causes the alignment controls to be unavailable, though each segment, depending on its orientation, has inherent left, middle, or right text alignment. The indent/outdent controls remain operable, and text entered in a given segment can be stacked by introducing a return.
One can enter continuous text, and that will overflow into the adjacent segment, pushing the segment divider to the right. Rather unwieldy though…
Anything fancier and one could suppress the header or footer in the Documents panel, and introduce a gridless, one/two row table in the same location, or a resized image in concert with an adjacent table. With both selected, one could then select the Arrange menu > Section {Layouts, Masters} > Move Objects to Section {Layout, Master} to place this new content below the text layer. One should test how this affects any export to Word visuals.