I recently finished building a big apple type strat that has 3/4" poplar boards 'butcher blocked' together with a flamed redwood front and poplar neck (!). The guitar is around 5 pounds and has unusually long acoustic sustain, almost twice that of my stock strat. OK, so there are other details. It has three CF rods, (inexpensive hobby store variety) embedded close to the three 'corners' of the neck. It also has a hand made single action truss mounted in the correct fashion, deep in the D and not touching anything other than at each end. The poplar and redwood both came from Homedepot and cost less than 15$ total. Ok, so I put a brazilian rosewood FB on it which is probably worth about $250. Hey, I had it lying around! I've built other guitars before this, but I wanted to try out some crazy stuff, like using poplar for a neck. The outcome was far better than expected. The guitar is in the hands of a proper shredder now, who likes it because it's light and has great tone and sustain.
I think you'll make a fine guitar out of plywood, even the neck. If you're worried about CF costing a lot, try your local hobby store, or some hobby places online. Stewmac and LMI do charge too much. Also, people who makes kites use CF a lot, I bet they'd be a good place to look.
A good thing to remember when thinking about the properties of any material and vibrations is, as an object is made stiffer, mass and internal damping interact less and less. If an object is infinitely stiff, your ear won't know whether it weighs an ounce or a ton. In fact, if an object can't flex, can it be said to be vibrating? Ouch, that hertz!