Could the OCTC(open circuit time constant) method estimate the current gain bandwidth?
Poles of ANY transfer functions of linear circuits depends only on passive components and not from the place where you probe voltages or currents.
Voltage sources must be shorted and current sources must be opened in order to evaluate poles.
To answer your question:
It doesn't really matter where you probe the output current gain: the cut-off frequency will be the same of the as the voltage gain.
Comment:
In an UNPOWERED linear circuit composed of R, L, C components only, the position of the poles in the Gauss plane depends only on the topolgy of the circuit.
If you want to add a voltage or current source to an unpowered circuit you have to be careful. The voltage source must not alter the topology of the circuit.
How to determine if a voltage or current source, once added, modify the topology of the unpowered circuit?
Voltage sources can be added as series elements. In this way, once you turn them off they disappear without leaving a stray short circuit.
Current sources can be added as parallel elements or elements from one node to another.
Zeros instead do depends on the position of input and output.