Can 300 ADC damage a battery wire (4AWG) rated for 60VDC, 150ADC if 300ADC @5VDC is passed for 2 seconds?
In practice, the insulation won't get hot enough to melt.
You can get an estimate of how long the cable can withstand a current by applying the adiabatic equation.
Given that 4AWG is around 25mm², and PVC cable is normally rated for 70°C.  Assume a conservative value of k (from the web site linked above) of 103 for PVC copper cable that's already hot.
We get t = k²A² / I² = 103².25² / 300² = 73 seconds.  Which is well above 2 seconds!