I cant see any reason why it would hurt to add more air stones. How much it would help and how many you need is another question. How quickly the water will lose oxygen depends on a lot of things (water temp, how many plants, how fast the water is running etc. I have seen people use this solution some say it works well, i haven't tried it myself. I would suggest trying the system without the extra stones with some fast growing plants and see at which point they start to show signs of oxygen deficiency, then add air stone there and see if the plants liven up.

I tend to try and design my systems to have some sort of periodic self oxygenation points like a 200-300mm drop every so often to stir up the water and force air into to stream. Not sure if your design will allow this or not.

I have a similar setup, it's considered NFT (nutrient film technique). basically the water flows over the roots, but the roots shouldn't be fully submerged. Unless you are doing something to back up the water, the roots will be washed by the water, but they're still exposed directly to air. I don't oxygenate at all. You don't really need to with this type of system. as the water runs through the pvc it picks up oxygen from the air. you have to consider that the surface area of the water is dramatically increased as it runs through the piping. and that's all the air stones do is run air past the water so that it picks up the oxygen.

I don't even use an air stone in the reservoir. the only time I had a problem was during the summer when the temperature of the water in the reservoir got up in the 80's. I got some root rot on some of the plants. but I just put some reflective mylar around the reservoir and the problem went away.