If you pack light you can probably make it work. That is backpack style camping, assuming you are not carrying group items. The biggest issue is going to be seating space with a relatively small frame size. Leg space occupies quite a bit of room on such a small boat. You might consider putting your cooler up in the front and use a seat such as the stadium chair (got mine with coupon for $26 at Sports Authority). This will allow the passenger to sit atop the cooler in the front with a comfortable backrest.
Your frame is pretty wide, you should be able to fit a 120qt cooler with ease. keep in mind 120Qts = 30 gallons =~ 200 lbs of weight when full. If the flows are high overloading your cat means its sluggish to maneuver, and difficult to fight the flow of strong currents while in the rapids. If the flows are low the push will be less but you will probably hit every shallow rock further complicating your maneuver.
so be sure to pack light or bite the bullet and get some longer, larger diameter tubes ...
Hey, if you want me to take a dump in a box and mark it "guaranteed", I will. I got spare time.