Four years later...
I was looking for the same situation.
Adb requires a network connection as it is a client-server connection where the Android device is the server and the computer the client.
To work around this, you need Termux (an Android terminal with package manager) and a local VPN such as Netguard. Root access is not required.
In Termux you can install a native Android version of adb which is step 1 by apt install android-tools.
But adb should make a network connection to the device itself. Then a VPN can be useful. VPNs operate locally, where the device acts as a VPN server such as for adblocking like Netguard. Then your device gets another network with another IP address, e.g. Netguard makes 10.1.10.1 which I use as an example (your VPN might issue a different address).
Run adb connect 10.1.10.1
The device might prompt (only once) with 'allow connections from computer ..blabla...' and consent this.
Then run adb connect 10.1.10.1:5555 and you are connected. Now adb commands can be run from the Termux command shell regardless on the device itself or via an SSH connection.
Note: Plugging in USB is still needed after reboot, unless you have Android 11+.