A friend of mine was just checked for his invasive species sticker when he went to put on Lake Lowell for a flatwater paddle. The lake is right near Boise and is frequented by power boaters, so it's not exactly the Middle Fork or Selway put-in. Nonetheless, the sherriff knew the scope of the law very well and insisted that kayaks (of any length) and inflatables over 10 ft. were not exempt. It's a $60 fine if they catch you without one and you might not be able to put on.
That said, there seems to be significantly less enforcement on Forest Service land. The Payettes might be an exception to that observation. Just buy one at an outfitter in Boise (Idaho River Sports) and save yourself some hassle and heartache if they do check you at the launch.
"A river is more than an amenity, it is a treasure."
-Oliver Wendell Holmes writing for the majority in New Jersey v. New York