Not with standard Windows sockets (Here are the styles available for combo boxes ).
As @ILMV said, Windows will clear the window up rather than down if there is not enough space in the box.
You can check this with notepad - go to format → font and drag the window down so that the Script combo box is just above the start menu. Click the combo box - it crashes.
If you want it to always fall, you will need to make your own.
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