Popup is a separate part of the AutoCompleteBox, so it should be possible to expand this beyond the width of the text box.
In Blend, right-click on AutoCompleteBox and choose Edit Template> Edit Copy, giving the new template a name.
Expand the Pop-up part in the Objects and Timeline window, and the grid below. Change the width of this grid to change the width of the pop-up content, while maintaining the current width of the text field).
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