Why would it, the lift has a flat surface on it so it would just press on the brace.
My lift doesn't fit inside the frame crossmember, so to have the brace inside it would be better for me.
Steve
With many (most?) lifts, the rear arm sits in the channel of the dog bone. This is the best balance point for standard sized jacks, and placing the arm in the channel also helps keep the bike from sliding around on the jack once it's elevated. When you fill that channel with one of these devices, the jack will have to either be moved forward to miss the bracket or be allowed to contact the new bracket. Either will affect the balance point and the leveling of the bike.
One other consideration, this also eliminates the ability to install other accessories which fit in that dog bone such as a center stand. Another thing to look at is the loss of clearance at the oil pan. From the photo's in the instructions it looks like the trans pan bracket would reduce ground clearance by nearly an inch. May be acceptable on a standard height bike, but since I've already dragged the pan on my SEEG more than once over whoops in parking lots I don't think this thing would be a great idea on a lowered bike. Other alternatives I've seen don't hang down this much.
Just some things to think about when comparing products. As noted earlier, they all will have a similar affect, just different ways to a similar result.
Jerry