nope, the cable pull ratio is mis-matched. the shifter is 10 speed mountain series so expects a 1.2 pull ratio derailleur. all shimano 9 speed rear derailleurs use a 1.7 pull ratio. see https://bike.bikegremlin.com/1278/bicycle-rear-derailleur-compatibility/#1
you will need a shimano dyna-sys 10 speed rear derailleur for that shift lever
I am using a Hifi Walker H2. It is a reasonable price, has bluetooth and no capacitive touch inputs. The UI is not great but the device is physically solid and works for me.
I pre-ordered a Tangara on their crowd funding. I am hopeful about the opensource hardware and software. Only reservation is capacitive touch scroll wheel.