If I were to bowl the bowling ball into the corner of the gutter to pick up a split (usually 7-10 split applies here), is it still legal if it goes in the gutter completely, comes out of the gutter, and hits the pin(s) ?
No, it would not be legal. If the ball goes into the gutter before reaching the pins, any pinfall that happen after the ball hits the gutter is not legal pinfall, therefore the pins either need to be stood back up(if on the first ball of the frame) or the shot counts as 0(if on the 2nd ball of the frame).
Rule 6b - Illegal Pinfall
6b. Illegal Pinfall
When any of the following occur, the delivery counts but the resulting pinfall does not:
A ball leaves the lane before reaching the pins.