Per the manufacturer of the Woodlink Slot n Pin Double Horizontal Rail Deck Clamp (SP8) the opening is 2.5” tall. If you wind the bracket all the way down to the top, it is 2 1/8”.
Per the manufacturer of the Woodlink Slot n Pin Double Horizontal Rail Desk Clamp (SP8), the maximum size that this would fit is 1 1/2" rail.
The Woodlink Slot n Pin Double Horizontal Rail Deck Clamp (SP8) opens up to a maximum of 2.5", so yes, it would work on a 2 x 4 deck rail.