FLC OF AN LTT CPR TURBOPROP RESPONDED TO A CLRNC FOR ANOTHER ACFT WITH SIMILAR SOUNDING CALL SIGN. A DSCNT WAS STARTED ON AN ILS APCH TOO EARLY AND DOWN TO 1000 FT BELOW ASSIGNED ALT PRIOR TO CATCHING THEIR MISTAKE; VERIFYING THE MISTAKE WITH ATC; AND THEN RETURNING TO ASSIGNED ALT.

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RECURRENT TRAINING WAS BEING CONDUCTED IN MODERATE TO HVY RAIN WITH CONTINUOUS MODERATE TURB. AFTER LNDG AT CAE; FOLLOWING AN ILS APCH; I ASKED THE TRAINING INSTRUCTOR IF HE WANTED TO FLY THE LEG BACK TO GMU FROM THE R SEAT. HE RESPONDED THAT HE WOULD ENJOY THE CHANCE TO GET SOME 'STICK' TIME. THE FLT PROCEEDED NORMALLY TO GMU IN THE ABOVE MENTIONED WX CONDITIONS. I WAS WORKING THE RADIOS FROM THE L SEAT AND OPERATING THE WX RADIOS. THE APCH CTLR AT GREEN ISSUED WHAT I THOUGHT WAS AN APCH CLRNC TO GMU. WE DSNDED FROM 4000 FT TOWARD 2500 FT AND BELIEVED WE WERE CLRED FOR AN ILS RWY 36 AT GMU. PASSING 3000 FT I BECAME SUSPICIOUS; BASED ON OUR FMS DISPLACED LOCATION AND ADF BEARING TO THE LOM; THAT WE HAD ACCEPTED AN APCH CLRNC FOR ANOTHER ACFT WITH A VERY SIMILAR CALL SIGN. I QUERIED THE CTLR AND HE VERIFIED THAT THE CLRNC WAS NOT FOR US. WE CLBED IMMEDIATELY TO 4000 FT. I BELIEVE THIS INCIDENT WAS CAUSED BY OUR PLT ROLE REVERSALS DURING A TIME OF HIGH WORKLOAD DUE TO WX. ALSO THE APCH CTLR DID NOT CORRECT MY INCORRECT READBACK OF THE APCH CLRNC. OUR SITUATIONAL AWARENESS; FMS AND ADF; HELPED US TO QUESTION IF WE WERE INDEED CLRED FOR THE APCH.