Yes, there are no restrictions on what thickness the wood on the shipping crate must be. However, you want to make sure that you keep your weight under 400 lbs so that you won't have to pay extra for your crate.
There is a supplemental document to Section 4 of the Game Manual (found here:
http://www.usfirst.org/uploadedFiles...ndations. doc) that gives some suggestions on how to build and ship your crate.
This is what it said about thickness of wood.
All crates should:
a. Be sturdily built to prevent damage to your equipment
b. Use 3/8 or 1/2 plywood or 3/8 or 1/2 Oriented Strand Board (OSB), a solid panel product of consistent quality with no laps, gaps, or voids.
Crate building cautions:
a) Medium density fiberboard (MDF) is not recommended for crate building because the material makes crate construction too heavy, and MDF can be dangerous to use if the correct safety precautions are not taken. MDF contains a substance called urea formaldehyde, which may be released from the material through cutting and sanding and cause irritation to the eyes and lungs.
b) Dont use particleboard because it collects moisture that adds weight and may cause the crate to fall apart. Remember, your crate may be exposed to the elements when loading and unloading trucks.
Hope this helps!!
__________________
Team Overdrive FTC #2753
A big thank you to all of our sponsors and supporters!!
2006/2007: FVC #3179 - New Jersey Champions
2007/2008: FTC #74 - Ohio, Delaware, New Jersey, New York, and World Champions
2009: FRC #2753 - New Jersey Champions &
Archimedes Division Champions 
PARC champs, BRBR champs, & Brunswick Eruption champs
2010: FRC #2753 - NJ semifinalists, Philly semifinalists, ranked 44th in Archimedes division
2011: FTC #2753 - DE semi-finalists, NJ division finalists