300SDL- would a non-funtioning aux fan trip a/c compressor?

[a2aa]

Would a non functioning auxillary fan trip the a/c compressor >1min after the a/c is turned on?

At first, turning the engine off and on again would reset the system and re engage the a/c compressor. Today, after some inspecting, I found out that the aux fan is faulty,thus it doesn't come on during start ups - (when head pressures are high), would this trigger the relay to dissengage the compressor clutch? Other wise, the system works beautifully. BTW , ambient temp in Texas now a days is 102 degrees.

Thanks for the help