The air pump electrical connector can be unplugged, and the vacuum line to the one-way air valve can be plugged, and the pulley will just spin on the idler bearing. This bearing will go out every 10-12 years, but is pretty easy and cheap to replace. This approach is one way to permanently deal with a failing emissions pump. As stated, will not effect emissions cause they test with a warm engine. But, you are technically in violation of the emission law.

The EGR valve is another story; it should be functioning to help maintain factory fuel mixture settings and lower combustion chamber temps at cruise RPM. You might get ping in hot weather if it's not functioning. The EGR actually does not open at the emission test speeds used in Texas (12 MPH & 22 MPH i think), so it does not come into play during the test. The common failure modes I have seen are the pintle not moving when you apply vacuum to the nipple (ruptured diaphragm), or a clogged passage where
the EGR pipe enters the underside of the intake manifold. Both will have the same effect - no change in idle when vacuum is applied to the EGR. If it is functioning and the pipe is clear the idle will change very noticeably when vacuum is applied.

DG