Correct
I was flying CX,but got my boarding pass from T4, travelled landside to T2, passed immigration at T2, went to T1 QF and BA Lounge

You may be checked by the staff at the entrance to the Shuttle back to T4 if you do it this way, so maybe you should enter airside in T4 first, then go take the Shuttle to T2 I wasn't sure they would let people go from T4 to T2 as I previously heard reports of people rejected, therefore I used the method above. (I just mention I had ample amount of time, around 10-12 hours until my flight depart)