If it's in the back of a van, it's not being driven, towed, stored, or parked. It's being transported.
You could certainly make that argument. I'm not sure if it'd be considered valid by the courts though, considering the existence of a specific permit that explicitly allows the transportation of a race vehicle.
Also, the direct CVC (not the paraphrase from the FAQ of the CA DMV website) section 4000 says:
4000. (a) (1) No person shall drive, move, or leave standing upon a highway, or in an offstreet public parking facility, any motor vehicle...unless it is registered and the appropriate fees have been paid under this code or registered under the permanent trailer identification program, except that an off-highway motor vehicle which displays an identification plate or device issued by the department pursuant to Section 38010 may be driven, moved, or left standing in an offstreet public parking facility without being registered or paying registration fees.
I don't think that you could argue for it not being moved on a highway even in the back of a van. Of course, the officer would need probable cause to search the van, but that's easily arranged in today's world. :|
And just to cover all the bases:
Section 38010 lists the exceptions (CA Code: 4006, 4010, 4012, 4013, 4015, 4018, and 4019)
4006. A vehicle which is driven or moved upon a highway only for the purpose of crossing the highway from one property to another in accordance with a permit issued by the Department of Transportation is exempt from registration.
4010 is for construction equipment.
4012 is for cemetery equipment. (Might be able to sneak it in here...

)
4013 is forklift
4015 is firefighting
4018 is logging equipment
4019 is for golf carts
This is also convenient proof that your race transportation permit is a valid registration, as it specifically allows transportation of the vehicle on highways, which is illegal if the vehicle is not registered
And now you have more information than you ever wanted to know about the CA DMV.
