To reproduce:

Add a RadMultiColumnComboBox with two rows. Open the dropdown, you will see no scrollbars, open it again and scrollbars will be visible.

Workaround:

Use the following custom class:

public class MCCB : RadMultiColumnComboBox
{
    protected override RadMultiColumnComboBoxElement CreateMultiColumnComboBoxElement()
    {
        return new MCCBElement();
    }
}

public class MCCBElement : RadMultiColumnComboBoxElement
{
    protected override Size GetPopupSize(RadPopupControlBase popup, bool measure)
    {
        Size baseSize = base.GetPopupSize(popup, measure);

        RadScrollBarElement hScrollBarElement = this.EditorControl.TableElement.HScrollBar;
        baseSize.Height += (int)hScrollBarElement.ControlBoundingRectangle.Size.Height;

        return baseSize;
    }

    protected override Type ThemeEffectiveType
    {
        get
        {
            return typeof(RadMultiColumnComboBoxElement);
        }
    }
}