I am getting ready to have my '88 F250 460 EFI motor and tranny rebuilt. I checked with the local exhaust shop about replacing the factory exhaust manifolds with headers. There are several pipes that run from the exhaust and cat to the fuel injection system. I want to eliminate them but he says that the EFI will run poorly w/o it. I hate that Y pipe that Ford has that runs under the oil pan. His shop has been in business since the 70's

 

Lot's of threads in storage about the removal of these systems, the vacuum lines, their electrical actuator leads, and their sensor inputs.

On your 1988 460 it can be done quite successfully.

Other vehicles not so much.

 

The thermactor air injection system is designed to add oxygen to the exhaust to help the stock cats heat up faster at cold start to burn of excess hydrocarbons, after the cats reach operating temp the system bypasses the exhaust and the air is simply dumped back to atmosphere. If the stock cats have been removed or replaced this system no longer serves any purpose, aftermarket cats don't need the extra air and can even overheat with it.
This system is designed not to interfere with the EFI system, it only injects air at the heads or exhaust manifolds immediately after cold start and up until the engine goes into closed loop and starts taking readings from the O2 sensors, after than the system continues to inject air directly to the cats only so as to avoid corrupting the O2 sensor readings. That means the whole system can be deleted without having any effect on the EFI system, the only requirements are that there be absolutely no air leaks in the exhaust system upstream of the O2 sensor, all vacuum lines plugged, and the TAB and TAD control solenoids must remain electrically connected to minimize codes.. some codes may still get set but they won't be significant enough to set the check engine light.