tubes are one of those unnecessary things that you do only if you have the time. I don’t think that you need them, or could finish them, in time for the entry deadline.
Personally, I think you see the whole robot image mre clearly when your robot is unfolded.
If you find the time to model the tubes I would first go through the document titled something like Getting Started with Routed Systems.pdf that you can find in the Inventor folder on your hard drive (I can’t remember the exact name of the file but if you search on *.pdf you should find it.) There is an example of routing stainless steel tubing that would be appropriate for your design - just change the color to match your tubing.