The closure_phase_bias.py does not require connected components to run, because it calls isce2 within mintpy to unwrap the generated closure phase, which can be time-consuming.
The regular smallbaselineApp.py, which does not include closure_phase_bias.py within it yet, does require the connected component for the phase unwrapping error correction step. Although advanced users could re-unwrap using isce2/snaphu for hyp3/gamma products, this is not built-in for smallbaselineApp.py.
I hope this clears things up.
Yunjun