I assume you are refering to the roof rack snowboard carriers that clamps down on the snowboards, then yes it's safe to put then without bindings. I've never had a snowboard move back while being clamped in, this is from my experience with my equiptment. Just make sure the rubber in the rack is really clamped down tight.
As everyone has stated, it's fine. I've done it. The rubber on the clamps will prevent the board from moving and the nose and tail curves of the board will prevent it from slipping out (just make sure you lock the clamps down).
What is going to happen to your board on the rack is much less than what you are going to do it on the hill. It's a non issue. Plus, a board and/or skis in a vehicle can do bad thing to body parts should you end up in a metal bending accident.