I have not read the entire text of the long gun on carry restrictions, but by the synopsis that I have read, it would be illegal because the rack doesn't qualify as a container or case.
Aside from the legal issues, it is just not a smart thing to do. Good guys, bad guys, and everyone in between knows you have a gun. Are you planning on keeping your truck in sight every second? You are inviting theft, and every cop that sees it now has the legal authority to stop you and inspect the weapon.
If You Heard The Shot, You Weren't The Target