How do you know when to CAD vs draw up on paper quickly

Here's a good way to think about it: Would you trust yourself riding in a car you didn't do CAD for, and only sketched it roughly out?

There's a fun exercise you can do to test this out. Have one of your team members go grab a random part from an old robot, mainly one that was Milled simply. Have him/her sketch it out "quickly" on a piece of paper, with all the dimensions THEY think you'd need to make it. Give that drawing to a team member who has not seen what part it's drawn from, and have them try to make it. Unless your student has taken some drafting courses, or is quite gifted in conveying all the details of the part on a sheet of paper, I'm pretty sure there will be errors.

If you sketch it out as you go, you'll always be building under the pressure of the clock. If you CAD it entirely, all you have to do is put the model together. Motion can be tested, speeds can be calculated, and interference can be looked for before hand. You'll end up with a more honed and precise machine, which should elevate your level of competitiveness.