Android Things will use the latest version of Bluetooth called Bluetooth Low Energy and the only similarity between the two is that they have Bluetooth in the name!
Can I use Android Things with a Bluetooth connection?
Yes, well a Bluetooth Low Energy connection
https://www.link-labs.com/bluetooth-vs-bluetooth-low-energy/
In summary, Bluetooth and Bluetooth Low Energy (BLE) are used for very different purposes. Bluetooth can handle a lot of data, but consumes battery life quickly and costs a lot more. BLE is used for applications that do not need to exchange large amounts of data, and can therefore run on battery power for years at a cheaper cost. It all depends on what you’re trying to accomplish.
Everything you need to know about BLE is written here:
https://developer.android.com/guide/topics/connectivity/bluetooth-le.html
how can I enable Bluetooth without an input device?
You do not pair BLE devices like you used to with the older Bluetooth (but you can use Bonding). Check this out:
Android Bluetooth Low Energy Pairing
https://stackoverflow.com/a/20093695/413127
But as stated by @shalafi Android Things doesn't currently support Bluetooth