I am a professional deck builder in Washington state and have been building decks for 20 years. Pressure treated wood in necessary for all framing of a deck otherwise it will rot out in 5+years. I replace decks all the time where non-treated wood was used.
Since you're going to use the treated lumber, you must make sure that all fasteners and supports, nail, bolts, hangers, connectors, flashing, whatever, have to be rated for contact with current chemicals for treatment or fasteners don't directly contact the wood, using epdm membrane or such. Standard is hot, double dipped galvanized fasteners and hangers. Regular joist hangers, for example, will corrode faster. The chemicals in the treated lumber is very corrosive to metals and you might as well use the cedar if fasteners are wrong kinds. If hidden deck fasteners are used, make sure the instruction says they will not corrode if in contact with PT. Coated nail gun nails are the worst. Do not allow the deck to be finished with nail gun nails.