Not at all, you are thinking correctly.
Are you planning to use this on the wall too? This material is really supposed to go on a stud wall, where you build a frame around the room (150mm from the wall) and you then place it over the frame.
If you build a stud wall and place the skirting over the first layer then you have no problem, just make sure you use screws with large heads, this will stop you punching right though the skirting board and through the membrane creating a hole.
About the sound passing down the wall and through the board - No problem as the bottom layer will stop it on the floor, which is what you are really trying to do here. Double up on the floor layering if you can. I think thats what you meant above
It will be fine, just remember that the room will leak sound at its weakest point. Have you considered the door?