Common base circuit with zero supply voltage
Here is your circuit redrawn more conventionally:-







simulate this circuit &ndash; Schematic created using CircuitLab

The Collector can pull current through R1 to the Emitter and Vin-, so the output voltage will (almost) equal the input voltage. 

And now the same circuit, but with two diodes instead of a transistor:-







simulate this circuit

There is no way for the "collector" to pull down, so the output will remain at 0V. 

Conclusion: the 'two diodes model' does not represent a BJT in saturation.