FLC OF AN LGT ACR ACFT HAD STUCK MIKE RESULTING IN LTSS FROM ANOTHER ACFT ON APCH.

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THIS WAS A SCHEDULED ACR FLT FROM BTV TO ORD. FO WAS PLT AT CTLS AND DEP WAS NORMAL. UPON CAPT'S FIRST RADIO CALL TO DEP; THERE WAS A LOUD SQUEAL AND THE ACR HEADSET I WAS USING BECAME UNUSABLE. FO MADE RADIO CALLS WHILE I PLUGGED IN SPARE HAND MIKE AND HEADSET (WE USED A BOOM MIKE). THIS ARRANGEMENT WORKED WELL ENRTE AND WE SENT COMPANY A MAINT MESSAGE REGARDING DEFECTIVE HEADSET. ORD WAS LNDG RWY 22L; RWY 22R WITH GUSTY WINDS OUT OF S. WERE VECTORED FOR ILS RWY 22R APCH WITH WX OF 35 SCATTERED; 7 MI VISIBILITY IN HAZE. AT ABOUT 19 MI FINAL WE WERE 'CLRED FOR RWY 22R ILS CALL TWR AT RIDGE OM.' I ACKNOWLEDGED CLRNC AND WE GOT BUSY CONFIGURING FOR APCH AND BRIEFING SPECIAL PROCS FOR WIND. ABOUT 2 MI PRIOR TO THE OM WE RECEIVED A TCASII TA. WE OBSERVED AN ACFT APPROX 1/2 MI OFF OUR L; SAME ALT AND DIVERGING. AT THAT POINT I REALIZED THAT IT HAD BEEN VERY QUIET ON THE PREVIOUSLY BUSY APCH FREQ. I CALLED WITH A RADIO CHK AND WAS ADVISED WE HAD A STUCK MIKE THE LAST 10 MI AND JUST HAD A NEAR MISS. VISIBILITY WAS FAIRLY GOOD AND TFC WAS IN SIGHT AND WE WERE ON LOC AND GS RWY 22R AND TOOK NO EVASIVE ACTION. THERE WAS NO TCASII RA. THE CHAIN OF EVENTS STARTED ON DEP FROM BTV WHEN THE HEADSET THAT WE ALWAYS USE FAILED. THIS PUT ME IN A DIFFERENT SIT (HAND MIKE AND UNCOMFORTABLE HEAD PHONES) THAN WE USUALLY USE. THIS WAS NOT SIGNIFICANT BUT GAVE JUST ENOUGH OF A DIFFERENT PERSPECTIVE TO PERHAPS PREVENT ME FROM RECOGNIZING THE STUCK MIKE EARLIER. THE SIT ALSO WAS COMPOUNDED BY THE WINDY CONDITIONS AT ORD MAKING THE CREW PREOCCUPIED WITH THE APCH SO AS NOT TO RECOGNIZE THE STUCK MIKE. ALTHOUGH THIS WAS NOT A CLOSE 'NEAR MISS' IT COULD HAVE BEEN. TCASII WAS DOING ITS JOB ALTHOUGH IN THE BUSY TERMINAL AREAS SUCH AS ORD; IT IS OFTEN TURNED OFF DUE TO NUISANCE ADVISORIES ON PARALLEL APCHS. ORD APCH FREQ IS OFTEN CONGESTED AND THIS DEMONSTRATES WHAT CAN HAPPEN WHEN IT GETS BLOCKED.