You'll need the following declarations:

Option Explicit

Private Type Rect
    Left As Long
    Top As Long
    Right As Long
    Bottom As Long
End Type

Private Declare Function FindWindow Lib "User32" Alias "FindWindowA" (ByVal Class As String, ByVal Window As String) As Long
Private Declare Function ChildWindowFromPointEx Lib "User32" (ByVal Parent As Long, ByVal X As Long, ByVal Y As Long, ByVal Flags As Long) As Long
Private Declare Function GetDC Lib "User32" (ByVal hWnd As Long) As Long
Private Declare Function GetClipBox Lib "GDI32" (ByVal hWnd As Long, Rect As Rect) As Long
Private Declare Function GetClientRect Lib "User32" (ByVal hWnd As Long, Rect As Rect) As Long
Private Declare Function EqualRect Lib "User32" (A As Rect, B As Rect) As Long
Private Declare Function ReleaseDC Lib "User32" (ByVal hWnd As Long, ByVal hDC As Long) As Long
Private Const NullRegion = 1, SimpleRegion = 2, ComplexRegion = 3

In the procedure where you want to determine this, first you'll need to get the actual window. GetDesktopWindow doesn't return the right one, since the shell creates a child window that serves as the actual desktop, which in turn can have several others.

Dim Desktop As Long, DC As Long, Clip As Rect, Client As Rect, Child As Long
Desktop = FindWindow("Progman", "Program Manager")
    Child = ChildWindowFromPointEx(Desktop, 0, 0, 1)
    Select Case Child
    Case Desktop, 0: Exit Do
    End Select
    Desktop = Child

More complete code would check if the window at (0, 0) was actually the desktop-sized window we're looking for and not some small desktop widget that happens to be at that location. Now we need to check how much of it is visible. Raymond Chen tells us how:

DC = GetDC(Desktop)
If DC Then
    Select Case GetClipBox(DC, Clip)
    Case NullRegion
        'Fully covered, e.g. if a window is maximized.
    Case SimpleRegion
        GetClientRect hWnd, Client
        If EqualRect(Client, Clip) Then
            'This shouldn't normally happen, since even in auto-hide mode the taskbar partially covers it.
            'Rectangular area visible.
        End If
    Case ComplexRegion
        'Complex area visible.
    Case Else
        'This shouldn't happen - it signifies the function failed.
    End Select
    ReleaseDC Desktop, DC
    'Handle failure of GetDC here.
End If

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