GEAR UP APCH RESULTS IN NEAR GEAR UP LNDG. PROP STRIKES ON TWIN SMT; EVASIVE ACTION GAR PERFORMED.

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I WAS INSTRUCTING AN INST RATED PLT WHO WANTED TO GET SIGNED OFF FOR INSURANCE PURPOSES IN A PIPER CHEYENNE I. IN THE COURSE OF MY INSTRUCTION; IT WAS NECESSARY TO HAVE THE PLT FLY A COUPLE OF MANUAL ILS APCHS TO MAKE SURE HE HAD A FEEL FOR HOW THE ACFT BEHAVES DURING AN APCH. SINCE THE ACFT IS EQUIPPED WITH A 3-AXIS AUTOPLT; I FELT IT WAS NECESSARY TO INSTRUCT THE PLT ON THE CORRECT PROCS TO DOING A COUPLED ILS APCH SAFELY. THE CORRECT PROC ON DOING THE COUPLED APCH IS TO FIRST BECOME ESTABLISHED ON THE LOC BELOW THE GS AND ADD 15 DEGS OF FLAPS; THEN ENGAGE THE AUTOPLT ON THE NAV/LOC MODE AND WATCH FOR ACCEPTANCE OF THE GS MODE. THIS WAS DONE AND THE PLT WAS ESTABLISHED ON THE LOC AND GS. IN THIS MODE; THE GEAR IS TO BE EXTENDED WHEN THE GS INDICATOR ON THE HSI CTRS. MY ATTN WAS DIVERTED DURING THE TIME AT WHICH THE GS INDICATOR WOULD HAVE CTRED ON THE HSI; SO I DID NOT NOTICE THAT THE PLT HAD FAILED TO EXTEND THE GEAR. THE REASON MY ATTN WAS DIVERTED TO THIS EXTENT IS THAT AFTER THE CHEYENNE HAD BEEN CLRED FOR THE APCH; ATC CLRED 2 SLOW-FLYING TOMAHAWKS TO COMPLETE THEIR VFR PATTERN AND LAND AHEAD OF THE CHEYENNE. SINCE I KNEW THE APCH SPD OF THE TOMAHAWK TO BE AT OR ABOUT 60-65 KTS; AND SINCE THE MINIMUM ALLOWABLE APCH SPD FOR THE CHEYENNE IS 120 KTS; I WAS QUITE CONCERNED ABOUT INADVERTENTLY OVERTAKING AND MEETING THE TOMAHAWK PRIOR TO HIS LNDG. ACCORDINGLY; I WAS HEAVILY INVOLVED IN TRYING TO GET AND MAINTAIN VISUAL SEPARATION FROM THE TOMAHAWK; AS IS REQUIRED BY REG; NOTWITHSTANDING ATC'S CLRNCS. BY THE TIME THE TOMAHAWK COMPLETED HIS TOUCH AND GO; THE CHEYENNE WAS AT 300 FT AGL. THE PLT APPEARED CONFUSED AS TO HOW TO DISENGAGE THE AUTOPLT; SO I HAD MY ATTN REDIRECTED TO THE TASK OF DISENGAGING THE AUTOPLT. WHILE I WAS BUSY DISENGAGING THE AUTOPLT; THE PLT PROCEEDED TO ADD 45 DEGS OF FLAPS. THE ACFT WAS BEING FLOWN AT THE PROPER SINK RATE OF 700 FPM ON A 3 DEG GS WHEN THE FINAL FLAPS WERE ADDED. ACCORDINGLY; IT TOOK ONLY A MATTER OF 20-25 SECONDS FOR THE ACFT TO LOSE THE REMAINING 300 FT. BECAUSE MY ATTN HAD BEEN DIVERTED EARLIER BECAUSE OF THE ATC CLRNCS AND HAD BEEN DIVERTED LATER BECAUSE OF THE PLT'S DIFFICULTY IN DISCONNECTING THE AUTOPLT; I DID NOT NOTICE THAT THE GEAR HAD NOT BEEN EXTENDED. THIS WAS FURTHER AGGRAVATED BECAUSE THE CHEYENNE WE WERE FLYING HAS NO WARNING SYS TO LET THE PLT KNOW THE GEAR IS STILL UP IF FULL FLAPS ARE EXTENDED; EVEN THOUGH SUCH A WARNING SYS IS NOT INSTALLED ON THIS PARTICULAR ACFT. BY THE TIME I WAS ABLE TO GET MY ATTN REDIRECTED TO THE POS OF THE ACFT; IT WAS NEARING THE POINT AT WHICH THE ACFT WOULD LAND WITHOUT THE BENEFIT OF WHEELS. I THEN NOTICED THAT SPARKS WERE FLYING FROM THE TIPS OF BOTH PROPELLERS; SO I IMMEDIATELY ADDED TKOF TORQUE TO TRY TO AVOID DAMAGE TO THE ACFT. THE ACFT WAS SUCCESSFULLY FLOWN OUT OF THIS PREDICAMENT WITHOUT ANY ADDITIONAL DAMAGE TO THE ACFT AND WAS SUCCESSFULLY RETURNED TO IT'S HOME ARPT WHERE IT WAS LANDED WITHOUT FURTHER INCIDENT. I FEEL THAT THIS TYPE OF INCIDENT COULD BE AVOIDED IN THE FUTURE BY TAKING THE FOLLOWING REMEDIAL ACTIONS: (1) NO LNDG CHKLIST OF ANY TYPE WAS USED. IN THE FUTURE I WILL FORCE MY STUDENTS AND MYSELF TO USE PRE- LNDG CHKLISTS; PARTICULARLY WHEN FLYING A COMPLEX ACFT. (2) WHERE I HEAR ATC GIVING ANOTHER ACFT A CLRNC THAT WILL LIKELY CAUSE A CONFLICT BECAUSE OF AN EARLIER CLRNC I HAVE RECEIVED (OR MY STUDENT HAS RECEIVED); I WILL IMMEDIATELY SO ADVISE ATC THAT I AM NO LONGER ABLE TO COMPLY WITH THEIR CLRNC BECAUSE OF CONFLICTING CLRNCS THEY HAVE ISSUED RATHER THAN PROCEEDING TO FLY UNDER THE CLRNC.