Sharing my experience yesterday.
I printed my CX T4 BP at home and tried passing T1 and T2 immigration - no luck. The machine won't be able to recognize this boarding pass.
The only way to access to T1-3 is to go through immigration at T4 and take the shuttle bus to T2.
The T2 -> T4 shuttle bus frequency is ~10min during day time and ~24min at night (after 1am)