I have a '91 300 SE, which is a bit different I'm sure.
But my pump has a clutch pulley like the AC compressor, and only runs
about 1 minute after cold start. It pumps air directly into the exhaust manifold through the check valve and sttop valve, to heat the cat up sooner.
It was rattling a bit, so I disconnected the electrical connector, and also the vacuum line that opens the check valve. no issues at all after two years.
Smog check is not affected, since they run the check with a warm engine, and the pump is off anyway.

But to add another thought - my old '87 Vette pumped all the time, but had two switching valves that routed the air to:
- exhaust manifold when engine was cold.
- air cleaner when engine was hot - just somewhere to get rid of the air.
- a little tube with a silencer, leading outside - this was only routed under specific circumstances of quick off throttle, to avoid a backfire or something.
- I killed the whole thing and never saw any issues.

I think on an older, less sophisticated car like an '86, or my '91, or the '87 Vette, you could disconnect the whole thing and the computer would never notice. Effects would be slightly more emissions at cold start.

DG