Will a buck converter allow current to pass through if Vin is less than the configured output voltage?
Yes, many Buck regulators (including the TPS54308) will do this. As long as the input voltage doesn't trip a UVLO protection (either internal to the chip or part of your circuit), it will pass through at 100% duty cycle trying to reach the desired output voltage. If you want a higher cutoff voltage than the chip provides, you'll need an external circuit to measure the input and drive the EN pin accordingly. 

From your datasheet: