Well, I think you should reconsider that statement.
Will the compressor clutch work without it? Yes.
How long will the compressor clutch work without it? ???
How much longer will the compressor clutch last with this diode in place? A whole freaking lot longer.
That is the reason that I rescinded my original remark.
It does potentially suppress any popping due to compressor engaging, but the actual purpose is to keep the inductive flyback from the compressor disengaging from welding the clutch center and outer pieces together.
The link that I originally posted to Wikipedia should be a good place to start.
jjh242t nailed it. And, I wouldn't drive around with a working compressor intentionally shortening its life
(or at least the life of the clutch - which in most cases: clutch = compressor)