quote; all 3 pieces (sink, toilet and bathtub) will funnel to a single drain which is currently the drain for the toilet.
Your choice of terms is interesting, but inaccurate. You CANNOT "FUNNEL" the pipes to the existing toilet drain, and it will be IMPOSSIBLE to run the pipe from the toilet under the tub, unless you put the tub on a throne. Just because the pipe is 3 1/2" in diameter does NOT mean that is all the space you need. By the time you make the downward transition, the pipe will be at least 6" above the floor to the top of it, and you will have a VERY difficult time connecting the tub to that pipe and do it properly.