There are teams who do use CAD. As to how necessary it is, and the advantages and disadvantages, I'll let someone who actually builds robots anser. But, one of the awards given in FTC is the PTC Design Award, sponsored by PTC (obviously) who provides their software to FTC teams:
PTC Design Award
This judged award recognizes design elements of the robot that are both functional and aesthetic. All successful robots have innovative design aspects; however, the PTC Design Award is presented to teams that incorporate industrial design elements into their solution. These design elements could simplify the robot’s appearance by giving it a clean look, be decorative in nature, or otherwise express the creativity of the team. The winning design should not compromise the practical operation of the robots but complement its purpose. This award is sponsored by Parametric Technology Corporation (PTC), developers of the CAD tools, Creo and Mathcad. PTC gives licenses to the FTC student teams for these software products to help them with their designs. Use of these tools is not required to be eligible, however, teams that use them in their design are given extra consideration for this award.
Guidelines for the PTC Design Award
Team must submit an Engineering Notebook with detailed robot design drawings
Robot differentiates itself from others
Design is both aesthetic and functional
Well thought out basis for the design (why i.e. inspiration, function, etc.)
http://www.usfirst.org/roboticsprograms/ftc/ptcdesign