If you can load application software onto them, I think it's fair to say they are general purpose computing devices. (I say application software since something like a thermostat may have a general purpose "computer" inside them and that microcontroller may have a reflashable ROM, but few would classify the device as a general purpose computer.)

That said, not all general purpose computing devices are useful for all things. For example: you can, but probably aren't, going to use a mobile phone for a server. On the flip side: you can use a server to do your banking, but most people won't find it as convenient as using their phone for banking (even though banking from a stationary computer is far more convenient than it was in the days when you had to go to a branch). Likewise: mobile devices can be used for content creation, but I doubt that you would find many office workers jumping at the opportunity to use them in the place of a desktop or laptop. On the other hand: someone who is on the road a lot would probably appreciate their portability.