They'd have a pretty easy time ticketing you if they so chose. The California vehicle code says a flat bed is not a pickup. It doesn't say "except when displaying an out of state license". Not saying I agree with that, or that it would be enforced, or that you might explain your position and get off with a warning. But that is the law. It is no different in any other state. Some states you can't turn right after stopping on a red light. It doesn't matter what plate you happen to have on the car - that's just the law there.
Flatbeds and utility beds have been skipping the scales here for quite awhile, but enforcement seems to be picking up. I've rented a big van truck, drove it by the scales a few times knowing I was taking a risk. No one stopped me. But they might have, the next time.