I have awesome installed both on Ubuntu 17.10 and Debian 9. Awesome under Ubuntu looks like Ubuntu default theme; awesome under Debian looks like MATE (I have multiple window managers installed but it seems MATE is default). My questions are:
[meta] Awesome does not set the GTK theme. It is totally outside of the project scope and is done by either a background daemon provided by the distribution of a bunch of configuration file.
You have to understand that Awesome is not a DE and that it doesn't do DE things like setting GTK/Qt themes or running background daemons for various common tasks (display, network, sound, power). All of these tasks are performed by 3rd party components that are not part of AwesomeWM and do not interact with it.
DEs and distributions do a lot of magic while Awesome and other WMs (i3wm, OpenBOX, dmw) only provide a limited set of feature. This is done by design and even if such DE features were proposed to those WMs, they would be rejected as out of scope. Awesome provides a lot more features than other WMs, but still doesn't intend to become a DE.
The Arch Linux Wiki has a lot of good documentation on all the topics touched by your question.
On a final note, if you want to make Awesome itself prettier, look at how other users did it: