Invisible does help with visible tetris because when the scope of your memory is limited (non-photographic :C) you begin to recognize how collections of pieces fit together. If you become familiar with that, it doesn't take as much to memorize it. After a bit of invis, you'll start seeing patterns with larger groups of pieces (i.e. start with noticing JZ, LS, LO, JO and how they form a square with a missing corner, and then add an L/J and they'll make a 3x4 rectangle, etc.etc.)
Noticing these patterns transfer to visible tetris. It helped me lower my sprint time by a good 3 or 4 seconds.