No it should not.
This means you have a leak in the system, which is probally what killed the last pump. The vacuum pump on the SuperDuty Diesels is there to control the HVAC doors, and if you have the ESOF 4x4 then it operates the hubs. My first guess would be something to the hubs. I would start by disconnecting the line from the pump and plugging it. If the pump shuts off, start working down the line. I think there is a "manifold" the pump feeds with lines to the various areas. Disconnect each line from the manifold, one at a time and plug the vacant port. If the pump stops, that is the line that is leaking. Just trace that line down and fine the leak.