With the current state of the art in Artificial Intelligence (AI), I can't see it happening any time soon, although it will happen.
At the moment, the largest users of UAV technology are the military. These aircraft are by and large guided by human operators, effectively flight sim pilots, with an aircraft at the end of the signal. Where these aircraft will ultimately prove their strength is in their ability to exceed the limitations imposed on human pilots (eg. high acceleration and G forces, not having to write a letter to a grieving relative etc).
To some extent we are already seeing the use of AI in missile technology.
What they are not currently able to do with AI guided aircraft, is to "think" outside the paramaters they are programmed with. AI is unable to deal with situations that they have not been programmed to deal with.
Neural network technology can allow AI to "learn" from situations (to some degree). If an AI stuffs up an approach for example, it remembers what didn't work, and does better next time. If it leaves a smoking crater in the end of the runway, the data can be uploaded to another AI, which will not make the same mistake, and will learn from every subsequent mistake it makes as well.
So in theory, an AI could learn to fly a plane. It would depend on the technology advancing considerably.
Communication would be difficult, but once again, voice recognition technology is slowly advancing.
In reality, the biggest hurdle would be to persuade the punters that flying as a passenger under computer control is as safe, or safer, than flying under human control. Of course freight, coastwatching, survey work etc. would have less of a problem with this.
At this point, it is nowhere near safe enough, but one day, who knows?
People are fickle. As soon as enough people consider it safe enough, everybody else will follow, especially if they are able to save $1.50 in the process.