ACR CREW DSNDS BELOW GS ON A RUSHED APCH UNTIL QUERIED BY ATC.

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AFTER AN AB15 AM DEP; MY COPLT AND I WERE FINISHING UP OUR 8 HR DAY. THE TIME IS AF15 AM LCL AND WE ARE BEING VECTORED FOR AN ILS RWY 12R APCH. OUR POS WAS JUST OUTSIDE THE OM 4 MI IN TRAIL OF A B737 WHICH WAS ON THE SAME APCH. WE WERE HIGH AND HAD A TIGHT TURN ONTO FINAL. OUR HEADING WAS 230 DEGS. THE APCH CTLR'S INSTRUCTIONS WERE TO TURN L TO A 090 DEG HDG TO JOIN THE LOC; MAINTAIN 3000 FT UNTIL ESTABLISHED; CLRED FOR THE ILS RWY 12R APCH. IN ORDER TO CONFIGURE AND GET DOWN WE ELECTED TO USE A SPOILER DSCNT WITH A 45 DEG BANK TURN TO INTERCEPT. I JOINED THE LOC APPROX 1 MI FROM THE 'ALAMO' LOM AND CALLED FOR GEAR DOWN AND THE BEFORE LNDG CHKLIST. WHILE THE PNF WAS ACCOMPLISHING THE TASKS ON THE CHKLIST; I CONTINUED TO FOLLOW WHAT I BELIEVED TO BE A 'LIVE' GS INDICATION. TO MY SURPRISE IT WAS NOT. THE MINIMUM APCH ALT IS 3000 FT AND WE WERE AT 2700 FT AND DSNDING. THE APCH CTLR RADIOED 'SAY ALT.' THE PNF AT THIS POINT WAS FINISHED WITH HIS TASKS AND ANTICIPATING OUR DSCNT RADIOED 'WE ARE THROUGH 2500 FT.' HE; I AM SURE; BELIEVED THAT WE WERE ESTABLISHED ON THE ILS. I IMMEDIATELY SAW THE ERROR AND ARRESTED THE DSCNT AT 2550 FT MSL AND INITIATED AN IMMEDIATE CLB BACK TO 3000 FT. APCH CTL BROKE US OFF THE APCH AND RE-VECTORED US BACK ONTO THE LOC FOR A SECOND ATTEMPT. THIS TIME THE APCH WAS UNEVENTFUL AND ALL GS INDICATIONS WERE NORMAL. SOME FACTORS LEADING UP TO THIS EVENT ARE FATIGUE AND POOR SITUATIONAL AWARENESS. THE B737 AHEAD MAY HAVE CAUSED ERRONEOUS GS INDICATIONS; I DO NOT KNOW. HOWEVER; AWARENESS OF OUR POS AND A XCHK WITH THE GS INTERCEPT ALT WOULD HAVE AVERTED THIS POTENTIALLY HAZARDOUS SIT.