Note the diode doesn't actually give full protection- in the case the transistor has voltage at its emitter
you can still get backfeed across the E-B junction and damage the base-drive circuit.
No doubt there are still fault current paths, but when the input is grounded the diode in the OP's circuit will discharge the cap on the transistor emitter, so I don't see where the emitter voltage comes from to drive the E-B current. If there is charge on the base circuit there could be B-E and B-C current, but the base circuit is usually at a high enough impedance to limit the base current. But I'm imagining the rest of the circuit, so I could be wrong.
An example of this is a DC power supply charging 12V battery.
If mains is turned off, there is still 12V at the emitter and the transistor backfeeds with ~7V avalanche to the drive circuit, which usually causes damage. OP's diode will just keep the filter capacitor charged.
Which filter capacitor? The invisible one on the transistor collector? Yes it will, but the discharging cap I'm talking about is the invisible one attached to the emitter. I guess there ought to be a series diode at the output of your battery charger.
Anyway, back to the OP's question: It's better to match or exceed the current rating of the original diode -- it was probably selected for a reason.