ACR FLC STARTS DOWN GS BEFORE AUTH TO DO SO.

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ARRIVING IN IAH ON DAISETTA 3 ARR AFTER REDUCED REST NIGHT AT LGA. AT DAISETTA; CAPT COULD NOT GET IN ON APCH FREQ DUE TO CONGESTION. WHEN HE WAS FINALLY ABLE TO GET IN; WE WERE GIVEN A LOWER ALT; AN AIRSPD REDUCTION AND A VECTOR FOR APCH TO RWY 15L IN SHOTGUN FASHION. I SCRAMBLED TO GET DOWN AND SLOW DOWN IN A SHORT DISTANCE. AS WE WERE ABOUT TO LEVEL OFF WE WERE GIVEN ANOTHER ALT AND VECTOR TO INTERCEPT THE LOC. AS WE WERE INTERCEPTING THE LOC 1 - 1 1/2 DOTS BELOW GS; WE WERE CLRED FOR THE APCH APPROX 22-23 MI OUT AND 3 MI IN TRAIL OF OUR TFC. I BELIEVE DUE TO MY FATIGUE; FEELING THE PRESSURE TO GET DOWN AND SLOW DOWN AND OUR CLOSE PROX TO TFC; I HIT THE APCH BUTTON ON THE MCP AND WE CAPTURED THE GS JUST PRIOR TO MKAYE. THIS CAUSED US TO DSND BELOW 5000 FT JUST PRIOR TO MKAYE. AT FIRST; WE WERE BOTH SURPRISED AT GOING BELOW 5000 FT AND THEN REALIZED WE HAD CAPTURED THE GS WHEN WE DIDN'T WANT TO YET. I DISCONNECTED THE AUTOPLT AND THE CAPT RESET THE FLT DIRECTOR AND MCP AND WE FLEW THE REST OF THE APCH WITHOUT INCIDENT.