CAPT OF A B727 RESPONDED TO A GPWS WARNING BY INITIATING A CLB AND MISSED APCH PROC RESULTING IN AN ALT OVERSHOOT OF ASSIGNED ALT. THE GPWS WARNING WAS CAUSED BY TOO HIGH A DSCNT RATE WHILE ATTEMPTING TO SALVAGE THE EXECUTION OF AN ILS APCH.

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I WAS THE CAPT ON ACR FLT ORD-GSO. DSNDING INTO GSO; WE WERE VECTORED FOR THE ILS RWY 23 APCH. WE WERE CLOSE ABEAM AT 3000 FT MSL ON A HDG OF 050 DEGS (DOWNWIND) AND 14.7 DME FROM THE GSO VOR (10 NM FROM TOUCHDOWN) WHEN WE WERE GIVEN A HDG OF 200 DEGS TO INTERCEPT THE LOC. DURING THE TURN WE WERE TOO CLOSE AND IT WAS OBVIOUS THAT WE WERE SHOOTING THROUGH THE LOC; SO THE CTLR TOLD US TO COME FURTHER TO A HDG OF 260 DEGS TO INTERCEPT THE INBOUND COURSE OF 232 DEGS (30 DEG INTERCEPT). WE WERE CLRED TO MAINTAIN 3000 FT UNTIL ESTABLISHED. I INCREASED THE CUT TO 40 DEGS (270 DEG HDG) TO EXPEDITE THE INTERCEPT AND WAS STARTING DOWN (I WAS HIGH ON THE GS) WHEN THE FO REMINDED ME THAT WE WERE NOT YET ESTABLISHED. I LEVELED OFF AND THE COURSE CAME QUICKLY ALIVE AND I OVERSHOT. THE CTLR SAID THAT HE COULD GIVE US AN ASR APCH OR TURN US BACK FOR ANOTHER ATTEMPT. I TOLD THE FO THAT I THOUGHT THAT I COULD SALVAGE IT AND STARTED DOWN WHILE RE-INTERCEPTING THE LOC. AT THIS TIME; I WAS 2 DOTS HIGH ON THE GS. I DROPPED THE GEAR AND FLAPS 15 DEGS AND PULLED THE PWR BACK; FIGURING THAT I COULD DROP THROUGH THE CLOUD LAYER AT 2900 FT AND ACQUIRE THE FIELD. (THE WX WAS RPTED AS 1900 FT OVCST AND 5 MI VISIBILITY.) THE TOUCHDOWN ZONE WAS 890 FT MSL; SO I FIGURED THAT THE LAYER WAS THIN. I ENTERED THE OVCST WITH THE PWR BACK AND ABOUT 2000 FPM RATE OF DSCNT WHEN I HEARD A GPWS WARNING OF 'TERRAIN' FOLLOWED BY A 'PULL-UP.' I STARTED TO ARREST THE DSCNT WHEN THE FO REMINDED ME TO EXECUTE THE GPWS PROC AND GET OUT OF THERE. I PUSHED THE PWR UP AND THE FO FURTHER ADVANCED THEM TO GAR THRUST. WE WERE AT ABOUT 2100 FT MSL (1200 FT AGL) WHEN WE RECEIVED THE GPWS WARNING. WE TOLD THE CTLR THAT WE WERE GOING AROUND AND HE GAVE US AN ALT OF 3000 FT. I DID NOT HEAR THIS; AND BECAUSE I WAS STILL IN A HIGH PWR/PITCH CONFIGN FROM THE GPWS RECOVERY; I OVERSHOT THE ALT BY 360 FT; WHILE QUERYING THE CTLR ABOUT WHAT ALT HE WANTED. THE CTLR APOLOGIZED AND VECTORED US BACK AROUND FOR ANOTHER APCH. I BROKE OUT AT 400 FT ABOVE TOUCHDOWN AND MADE AN UNEVENTFUL LNDG. AT THE TIME OF THE INCIDENT; WE HAD BEEN ON DUTY FOR OVER 12 HRS WITH 7 HRS 30 MINS FLT TIME IN ADDITION TO NOT HAVING HAD AN ADEQUATE MEAL BREAK THE ENTIRE DAY.