Here are some interesting findings:

Test bed is a white background character with a white background mask.
MergePaint/And: White areas shown through.
And/MergePaint: White ares shown through; picture inverted.
And/Paint: White did not show through.
Paint/And: White didn't show through. Interesting though; Areas on the sprite that weren't white on the mask multiplied by background.
Paint/MergePaint: White areas didn't show through. Image inverted. Areas on the sprite that weren't white on the mask multiplied by background.
MergePaint/Paint: Nothing shown, absolutely white.
Copy: White did not show through.
Invert/And: Foreground multiplied by background. Background was then (after this) inverted.
And/Invert: Background inverted, white shown through. Foreground intact.
And/Erase: Same as And/Invert.