It should increase if one aligns the TT ball first and then aligns the TT putter to the ball, although I believe an alignment system like this is of greater benefit to those who at least check alignment with eyes directly over the ball/target line at some pointI wonder how much your alignment accuracy will increase using this putter and a Callaway TT ball vs a standard ball?
personally I don't align that way although I can see the TT putter being of benefit based on how I do align