HAWKER 800 CREW HAD A GPWS 'PULL UP' WARNING AFTER THEY DID NOT INTERCEPT THE LOC ON RWY 7 APCH AT SBA.

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THE CAPT (PF) AND MYSELF (PNF) WERE APCHING SBA FROM PUB IN A HAWKER 800 XP. THE TURB WAS LIGHT TO MODERATE WITH SEVERAL AREAS OF HVY RAIN INCLUDING ONE CELL ABOUT 10 MI W OF THE ARPT. SBA APCH HAD VECTORED US TO A R DOWNWIND FOR ILS RWY 7. AT APPROX 8-10 MI FROM THE ARPT; WE WERE DSNDED FROM 4000 FT TO 3000 FT AND GIVEN A HDG OF 050 DEGS TO INTERCEPT THE LOC INSIDE THE AREA OF HVY PRECIPITATION. WE DSNDED AT ABOUT 1500 FPM AND TURNED TO INTERCEPT. I BELIEVE THE PF HAD ARMED THE APCH MODE AND WAS USING AIRBRAKES TO EXPEDITE THE DSCNT FOR WHAT WAS BECOMING A HIGH; TIGHT TURN TO FINAL. SBA APCH DSNDED US TO 2000 FT MSL WITHIN JUST A FEW SECONDS; CLRED US FOR THE APCH AND HANDED US OFF TO THE TWR. TO THE BEST OF MY MEMORY; WE FLEW THROUGH THE LOC AT 3200 FT MSL DSNDING; WELL ABOVE THE GS; WITH THE FLT DIRECTOR STILL IN HDG AND THE LOC NOT CAPTURED. WE CONTINUED ON THIS HDG UNTIL FULL NEEDLE DEFLECTION TO THE R. I THEN SAID FULL DEFLECTION OR SOMETHING TO THAT EFFECT AND MISSED APCH; SINCE WE NOW SEEMED FAR ENOUGH OFF TO THE L THAT REESTABLISHING SEEMED UNLIKELY. I KEPT REPEATING; 'MISSED APCH; TURN R' UNTIL SBA ORDERED AN IMMEDIATE R TURN TO 120 DEGS. I SAID 120 DEGS AND SAID WE WERE GOING MISSED. THE PF TURNED BACK TOWARDS THE R. THE PLANE CROSSED OVER THE MARKER AROUND 2000 FT MSL DSNDING WITH GEAR UP; FLAPS UP AND AIRBRAKES PARTIALLY DEPLOYED. THE PF STARTED TO GRADUALLY FEED IN PWR AND RAISE THE NOSE; BUT WE WERE SLOW AND CONTINUING TO DSND. I WAS NOW YELLING; 'PWR; PWR!' AT ABOUT 800-900 FT MSL; I PULLED BACK AGGRESSIVELY ON THE YOKE AS THE GPWS ALERTED 'PULL UP; PULL UP.' IT WAS NOT UNTIL WE STARTED CLBING THAT I NOTICED THE AIRBRAKES WERE STILL PARTIALLY DEPLOYED. THE PF RETRACTED THEM AND WE CLBED TO 2000 FT ON A 120 DEG HDG. SBA TWR ASKED IF WE HAD TROUBLE RECEIVING THE LOC AS A PREVIOUSLY LNDG HAWKER HAD COMPLAINED ABOUT THE SIGNAL ALSO. I ASKED FOR A LONGER FINAL AND A GRADUAL TURN ON TO THE LOC. WE CAME BACK AROUND FOR A 15 MI FINAL THIS TIME FLYING THROUGH MODERATE RAIN AND +/-10 KTS WINDSHEAR BREAKING OUT AT ABOUT 300 FT AGL. THE CAUSE OF THE INCIDENT WAS DUE TO FATIGUE OF THE PLTS AT THE END OF A LONG DAY IN ROUGH WX AND APCH CTL'S TIGHT TURN TO AVOID AN AREA OF WX WHICH POINTED US HIGH AND FAST RIGHT AT RAPIDLY RISING TERRAIN.