FLT CREW OF MDT MAY HAVE TRIGGERED ATC LOW ALT ALERTS WHILE SHOOTING A NON PRECISION APCH TO A NON-TOWERED ARPT. DID NOT RECEIVE ALERT NOTIFICATION DUE TO SWITCHING TO ARPT ADVISORY FREQ WHEN CLRED FOR THE APCH.

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APCH CLRED US FOR A NON-PRECISION GPS A APCH TO A NON TOWERED ARPT. DURING THE APCH ATC HANDED US OFF TO THE ADVISORY FREQ FOR THE NON TOWERED DEST ARPT. ALL STEP-DOWN FIXES; ALTS AND MDA ALTS WERE FLOWN AS PER THE PUBLISHED APCH. THE APCH RESULTED IN A MISSED APCH. DURING THE MISSED APCH CONTACT WAS MADE WITH ATC AND VECTORS GIVEN TO THE ALTERNATE ARPT FOR A PRECISION APCH. AN UNEVENTFUL PRECISION APCH WAS COMPLETED AND LNDG MADE. UPON ENTERING THE FBO A FLT CREW NOTIFIED US THAT ATC HAD ATTEMPTED TO CONTACT US AFTER THEY HANDED US OFF TO ADVISORY FREQ REGARDING A LOW ALT ALERT. THE FLT CREW IN THE FBO WAS BEING VECTORED BEHIND US FOR THE SAME NON PRECISION APCH WE WERE FLYING. ONCE THEY HEARD US GO MISSED THEY DIVERTED TO THE SAME ALTERNATE ARPT AS US AND WERE ON THE SAME ATC FREQ. DURING THE MISSED APCH ATC DID NOT INFORM US OF ANY PREVIOUS LOW ALT ALERTS OR ANY NEW ALTIMETER SETTINGS. AFTER APPROX 30 MINS ON THE GND AT THE ALTERNATE ARPT THE WX IMPROVED AT THE ORIGINAL DEST ARPT. A SHORT FLT WAS MADE WITH FULL VECTORS FOR THE SAME NON-PRECISION GPS A APCH WITH A LNDG AND CANCELING OF IFR ON THE GND. ATC DID NOT NOTIFY US OF ANY ALT ALERTS.