Removing the smog pump is OK if you don't have a catalytic converter H pipe. If you do, the lack of a smog pump will cause the catalytic converters to clog and fail.
I have torn (and I do literally mean torn) a smog pump apart. There isn't much you can do to fix them once they seize up or start to make serious noise.
Thermactor Air System
Some review of how it works...
The Thermactor air pump (smog pump) supplies air to the heads or catalytic converters. This air helps break down the excess HC (hydrocarbons) and CO (carbon monoxide). The air supplied to the catalytic converters helps create the catalytic reaction that changes the HC & CO into CO2 and water vapor. Catalytic converters on 5.0 Mustangs are designed to use the extra air provided by the smog pump. Without the extra air, the catalytic converters will clog and fail.
The Thermactor air pump draws air from an inlet filter in the front of the pump. The smog pump puts air into the heads when the engine is cold and then into the catalytic converters when it is warm. The Thermactor control valves serve to direct the flow. The first valve, TAB (Thermactor Air Bypass) or AM1 valve) either dumps air to the atmosphere or passes it on to the second valve. The second valve, TAD (Thermactor Air Diverter valve or AM2 valve) directs it to the heads or the catalytic converters. Check valves located after the TAB & TAD solenoids prevent hot exhaust gases from damaging the control valves or pump in case of a backfire. The air serves to help consume any unburned hydrocarbons by supplying extra oxygen to the catalytic process. The computer tells the Thermactor Air System to open the Bypass valve at WOT (wide open throttle) minimizing engine drag. This dumps the pump's output to the atmosphere, and reduces the parasitic drag caused by the smog pump to about 2-4 HP at WOT. The Bypass valve also opens during deceleration to reduce or prevent backfires.
Computer operation & control for the Thermactor Air System
Automobile computers use current sink technology. They do not source power to any relay, solenoid or actuator like the IAC, fuel pump relay, or fuel injectors. Instead the computer provides a ground path for the positive battery voltage to get back to the battery negative terminal. That flow of power from positive to negative is what provides the energy to make the IAC, fuel pump relay, or fuel injectors work. No ground provided by the computer, then the actuators and relays don't operate.
One side of the any relay/actuator/solenoid in the engine compartment will be connected to a red wire that has 12-14 volts anytime the ignition switch is in the run position. The other side will have 12-14 volts when the relay/actuator/solenoid isn't turned on. Once the computer turns on the clamp side, the voltage on the computer side of the wire will drop down to 1 volt or less.
In order to test the TAD/TAB solenoids, you need to ground the white/red wire on the TAB solenoid or the light green/black wire on the TAD solenoid.
For 94-95 cars: the colors are different. The White/Red wire (TAB control) is White/Orange (Pin 31 on the PCM). The Green/Black wire (TAD control) should be Brown (pin 34 at the PCM). Thanks to HISSIN50 for this tip.
To test the computer, you can use a test light across the TAB or TAD wiring connectors and dump the codes. When you dump the codes, the computer does a self test that toggles every relay/actuator/solenoid on and off. When this happens, the test light will flicker.