Android - Can I enable USB debugging using adb?

I got it to work :)

NOTE: This requires unlocked bootloader.

• Connect the device to Mac or PC in recovery mode. (I had to map the process in my mind as the screen was broken).
• Now open terminal/CMD in computer and go to platform-tools/. type and enter ./adb devices to check if the device is connected in recovery mode.
• Now type ./adb shell mount data and ./adb shell mount system to mount the respective directories.
• Get the persist.sys.usb.config file in your system using ./adb pull /data/property/persist.sys.usb.config /Your directory
• Now open that file in a texteditor and edit it to mtp,adb and save.
• Now push the file back in the device; ./adb push /your-directory/persist.sys.usb.config /data/property
• Get the build.prop file; ./adb pull /system/build.prop /your-directory

• Add these lines:

  persist.service.adb.enable=1                                                    
  persist.service.debuggable=1
  persist.sys.usb.config=mtp,adb

• Push build.prop back into the device; ./adb push /your-dir/build.prop /system/

This way you enabled USB debugging on your device. But you still can't connect. Why? Because it asks for RSA verification. If you could view your display then you could easily tap on YES to authorize the device. I am currently figuring out to bypass this. I want to revive my dead phone badly. If you know any way to do this, please share :)

For the RSA verification that you asked to bypass, I don't know whether it would work in your device, but it worked in my little experiment. In Lollipop, the ADB keys (after authorization) are saved in /data/misc/adb/adb_keys. Your private key is saved in computer. In Linux the directory location is $HOME/.android/. On Windows that usually translates to %USERPROFILE%\.android, but keys might end up in C:\Windows\System32\config\systemprofile\.android in some cases. (Source)

There is a method described here by ashoke which might help out in bypassing the authorization.

However, in my Lollipop, the method varies. I noticed that in my primary and secondary Lollipop ROM the adb_keys had the same key actually. All I did was revoke the authorization from the secondary ROM (file deleted automatically ), disconnected device from PC, copied adb_keys from Primary ROM into secondary ROM, connected the device into PC, and voila! I wasn't asked for that authorization. I double checked the authorization using adb devices and it was all good.

Try the linked answer first. Authorize a different Android phone, copy its keys into your device from Recovery mode and see if it works.