yea, its in there. By memory, moving to S shows 4 on the display. Holding it like you stated, will get it up to 6. Just remember if you select 2 from a stop, you are not starting in 2, you start in 1 but it wont go any higher than 2.
Until I read it I thought it should start in 2, and stay in 2, but it didnt, so I read.
The s shift from what gathered to explain is like a range of gears. If you have it in 4th then you are giving the computer 4 gears to choose from. And it will not go into 5th or 6th. If you have it in 2 then it will only be able to use the first 2 gears for its calculation range.
Other side of things is this is great for downshifting, because you are lower the range of gears and that force the computer to drop a lower gear. (If not going to fast for the lower gear - It does have a failsafe folks)
Good news is on up shift it is not immeadiate because the computer still may deem it better in the lower gear, but run that tach up to 5,000 or 6,000 rpms and the computer will almost beg you for that s-shift up and go in right away.