No, This sounds like a defective or the wrong fuel pump! Test fuel pressure at idle, should be lower to mid-50 PSI range. Test during snap acceleration/power braking. Should be 60+ PSI
A rubber line needs to be installed in the system so that it is possible to pinch the feed and return fuel lines.
Then turn the key on to get pressure up, and when the pump shuts off, then block the lines and see if it holds pressure or still bleeds.
If pressure holds, then release one clamp at a time and see which line pressure bleeds back on.
If the pressure does not hold with the lines pinched, then there is a leak up in the engine.
NOTE: It is also important, (especially on this year) When replacing the fuel pump that the fuel pump connector harness be replaced with the one supplied with the replacement pump (this is why they include it because failure/overheating of the connector is common!
28 Year Master, L-1 Technician