If the background is not solid, you can try this trick, which unfortunately
makes the box uneditable (make a backup copy somewhere).
Make the box's fill a trasparent copy of the textbox and delete the text to
make only the fill visible:
1) Select the textbox
2) Copy it to clipboard
2) Check that no automatic size adjustments are on
3) Create an image fill for the textbox, from Clipboard
4) Make the fill transparent
5) Delete the contents (text) of the textbox