Let's just get a few things out of the way, because I see some statements that I disagree with:
1. Is the CAR purchase agreement is assignable? From what I understand, yes, both legally by it's own terms and in everyday practice. There is a specific paragraph in the standard CAR purchase agreement, as @Bryan Zuetel correctly stated, that provides that any assignment must be consented to by the seller via a separate written agreement. CAR even has their own assignment agreement you can include with the CAR purchase agreement, and this is what a escrow company generally needs to do an assignment. Some escrow companies prefer to use their own assignment form, and it's always signed by the seller because the escrow companies are used to the CAR purchase agreement that requires seller consent. The CAR purchase agreement is assignable, and CAR even has their own assignment agreement to do this. The assignment-friendly escrow companies I know of do assignment escrows all the time with these CAR forms.
2. Is wholesaling illegal in CA? As other lawyers have stated, it's complicated and it depends. You should consult with an attorney familiar with the legalities of wholesaling, what the B&P prohibits specifically, best practices, etc. There are certain practices that should keep you from being under the CBRE/DRE's radar and you should strictly follow them, but there are always risks no matter what. You want to reduce the risks as much as possible by using certain contractual terms in your agreement, being transparent to all parties about the assignment and what that means, how you structure the transaction, etc.