Hi Steve,
Unfortunately, not directly using the component. The Custom Framing properties (e.g. FrameVisible) will affect the frame of the control, but the client area is managed by Windows and it treats the csDropDownList style as special.
Now, as an alternative, you could use a custom VCL style for the combo box and get the appearance you are looking for. The new per-control VCL Styling could be very useful in this case where you could just customize the particular combo box that you are trying to color.
Ray