After performing a TPI to carb swap is the fuel delivery circuit supposed to work as it did before the swap?

All the components are still there. Oil pressure sensor, Fp relay, ECM etc.

My issue is that the FP does initialize when I key on. The car starts and runs dies shortly because the fuel pump does not come back on. I understand that normally the Oil pressure sending unit would signal the circuit to come on and power the FP, but this is not happening.

I want to make sure that this sould happen after a swap before I go out and spend money on a Oil pressure sensor. Rather then hot hiring the FP relay if that is required.

 

You can test the oil pressure switch easily. It has three wires but you are interested only in two: the orange (power supply) and the grey (power to the fuel pump).

You can test that you have constant 12V on the orange wire at all times.
You can determine whether your sensor is bad by pulling the connector off the sender and shorting the orange and grey wires. If the fuel pump comes on, it most likely means that the switch/sender is bad (). Does your oil pressure gauge read right?

Let us know.
Lou