I've flown "commercial" with the pinnacle full of crap and had no problems. However, that was on Penn Air, and in-state.
Pretty sure that different rules apply, because when I showed up at the gate (late of course) and told them I had a handgun, unloaded and in a locked case, they said something to the effect of "We don't care, now pack that thing down to the gate before you miss the final boarding."
Were I in your shoes, I'd likely put it in a duffel or wrap it in a plastic bag, just to avoid snagging straps. But I wouldn't worry too much... you can't go to the Anchorage airport in the fall without seeing lots of frame packs.
