Relaton between IB, α and ICO near cut-off region for a bjt in CE mode
Equation 3 is totally derivable from eq2 and eq1 so the question really is should equation 2 be valid in all regions of operation.

In detail, equation 2 is saying collector current comprises the (large normally) fraction of emitter current that flows through the collector + leakage current through the collector-base reversed junction.

And, as far as I remember this is valid under in all regions of operation that I can think of.

This page might be useful.