PLT FILED IFR FLT PLAN FM WASHINGTON, DC, TO ROCKY MT, NC, & DEPD AT 0626 EDT. AT 0731 (BFR RCHG ROCKY MT), HE RADIOED HE WAS HAVING '. . . A LITTLE TROUBLE BREATHING . . .' & ASKED ABT THE DSTC TO ROCKY MT. THE CTLR ADZD ROCKY MT WAS ABT 17 MIN (FLYING TIME) AWAY; THEN HE RCVD NO FURTHER COM FM THE ACFT. IT CONTD SOUTH AT 10,000' MSL (SPD ABT 150 KTS) & WENT OVR THE OCEAN. MIL ACFT IN THE AREA WERE VCTRD TO INTERCEPT & ESCORT THE PLANE. INTERCEPTING PLTS NOTED A PERSON IN THE ACFT WITH HIS HEAD BACK IN A RECLINED PSN. THEY NOTED LITTLE MOVEMENT FM THE PERSON, THO HE MOVED THE SUN VISOR FM THE SIDE WINDOW TO THE STOWED PSN. SUBSEQUENTLY, THE ACFT'S SPD SLOWED TO 110 KTS. AT 1219, IT BGN DSCNDG & ENTERED A DSCNDG SPIRAL. AT 1227, THE ACFT TOUCHED DWN IN THE OCEAN (APRX 10 MI EAST OF ROCK SOUND, BAHAMAS) IN A WINGS LEVEL ATTITUDE. AFTER STOPPING, THE ACFT SANK, BUT RESCUE PSNL RETRIEVED THE PLT. HE WAS IN SHOCK WITH A GUNSHOT WOUND IN HIS ABDOMEN, RIB CAGE & L ARM. AT 1550, HE WAS HOSPITALIZED WITH INDCNS OF FULLY DEVELOPED PERITONITIS.